<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>





<b>set </b><font color="Maroon">T1</font> = <span class="p1">{<span class="default"> <font color="Olive">u</font> where <font color="Olive">u</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> :  ex <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Olive">u</font> <a href="tarski.html#R1">c=</a> <font color="Olive">v</font> ) </span>}</span> ;<br/>
<b>set </b><font color="Maroon">T2</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">v</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> : <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> </span>}</span> ;<br/>
<b>set </b><font color="Maroon">T3</font> = <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <span class="p2">(<span class="default"><a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font></span>)</span>;<br/>
<a NAME="E1:17"/><i><font color="Green">E25</font></i>: 
 <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">{<span class="default"> <font color="Olive">u</font> where <font color="Olive">u</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> :  ex <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Olive">u</font> <a href="tarski.html#R1">c=</a> <font color="Olive">v</font> ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">v</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> : <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> </span>}</span> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <span class="p3">(<span class="default"><a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<b>thus </b><a NAME="E2:17"/>
(  not <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">A</font></span>)</span> or ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> ) or  ex <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Z</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Z</font> or <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Olive">Z</font> ) ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">A</font></span>)</span>
 ;<br/>

<a NAME="E2:17_1"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">u</font> where <font color="Olive">u</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> :  ex <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Olive">u</font> <a href="tarski.html#R1">c=</a> <font color="Olive">v</font> ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">v</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> : <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> </span>}</span>  or <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <span class="p2">(<span class="default"><a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><i><font color="Green">E29</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">u</font> where <font color="Olive">u</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> :  ex <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Olive">u</font> <a href="tarski.html#R1">c=</a> <font color="Olive">v</font> ) </span>}</span> 
 ;<br/><a NAME="E2:17_1_1"/><b>then </b>
 ex <font color="Olive">u</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> st <br/>( <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> <font color="Olive">u</font> &amp;  ex <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Olive">u</font> <a href="tarski.html#R1">c=</a> <font color="Olive">v</font> ) )
 ;<br/><b>hence </b><a NAME="E3:17_1_1"/>
 ex <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Z</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Z</font> or <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Olive">Z</font> ) )
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green">E31</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1_2"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">v</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> : <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> </span>}</span> 
 ;<br/><a NAME="E2:17_1_2"/><b>then </b>
 ex <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> st <br/>( <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Olive">v</font> &amp; <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> )
 ;<br/><b>hence </b><a NAME="E3:17_1_2"/>
 ex <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Z</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Z</font> or <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Olive">Z</font> ) )
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1_3"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <span class="p2">(<span class="default"><a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font></span>)</span>
 ;<br/><a NAME="E2:17_1_3"/><b>then </b>
( <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font></span>)</span> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E3:17_1_3"/>
( ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> ) or  ex <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Z</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Z</font> or <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Olive">Z</font> ) ) )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:17_1"/>
( ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> ) or  ex <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Z</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Z</font> or <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Olive">Z</font> ) ) )
 <b>by </b><i>, , , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:17"/><i><font color="Green">E32</font></i>: 
( ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> ) or  ex <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Z</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Z</font> or <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Olive">Z</font> ) ) )
 ;<br/>

<div><i><font color="Green">E33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_2"/>
( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> )
 ;<br/><a NAME="E2:17_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <span class="p2">(<span class="default"><a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E3:17_2"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">Z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E1:17_3"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">Z</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; ( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font> or <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Z</font> ) )
 ;<br/><b>reconsider </b><font color="Maroon">Z</font> = <font color="Maroon">Z</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">Y</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> <b>by </b><i>, , </i>;<br/><div><i><font color="Green">E35</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_3_1"/>
<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font>
 ;<br/><a NAME="E2:17_3_1"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">u</font> where <font color="Olive">u</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> :  ex <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Olive">u</font> <a href="tarski.html#R1">c=</a> <font color="Olive">v</font> ) </span>}</span> 
 <b>by </b><i/>;<br/><a NAME="E3:17_3_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">u</font> where <font color="Olive">u</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> :  ex <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Olive">u</font> <a href="tarski.html#R1">c=</a> <font color="Olive">v</font> ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">v</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> : <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E4:17_3_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_3_2"/>
<font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Z</font>
 ;<br/><a NAME="E2:17_3_2"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">v</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> : <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> </span>}</span> 
 <b>by </b><i/>;<br/><a NAME="E3:17_3_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">u</font> where <font color="Olive">u</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> :  ex <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> &amp; <font color="Olive">u</font> <a href="tarski.html#R1">c=</a> <font color="Olive">v</font> ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Olive">v</font></span>)</span> where <font color="Olive">v</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font> : <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E4:17_3_2"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:17_3"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:17"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


</div>
