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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">F</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">BB</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:99"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span> where <font color="Olive">a</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Olive">b</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB</font> &amp; <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> holds <br/><font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> </span>}</span> 
 ;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Maroon">y</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:99_1"/>
<span class="p1"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="armstrng.html#K6" target="_self">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 ;<br/><b>then consider </b><font color="Maroon">a</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Maroon">b</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E3:99_1"/><i><font color="Green">E34</font></i>: 
<span class="p1"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="armstrng.html#K6" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span>
 <b>and </b><br/><a NAME="E4:99_1"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB</font> &amp; <font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> holds <br/><font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font>
 <b>by </b><i/>;<br/><a NAME="E5:99_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><b>hence </b><a NAME="E6:99_1"/>
for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB</font> &amp; <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> holds <br/><font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:99"/>
for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB</font> &amp; <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> holds <br/><font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font>
 ;<br/>

<b>hence </b><a NAME="E4:99"/>
<span class="p1"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="armstrng.html#K6" target="_self">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 <b>by </b><i/>;<br/>


</div>
