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

<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font> iff  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font> )</span><br/>



<b>thus </b><a NAME="E1:74"/>
( <font color="Maroon" title="c1">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font> implies  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font> implies <font color="Maroon" title="c1">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:74_1"/><i><font color="Green" title="E53">A1</font></i>: 
<font color="Maroon" title="c1">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font></span><br/>

<b>assume </b><a NAME="E2:74_1"/>
not  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:74_1"/><b>then </b>
 <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="classes2.html#T57" target="_self" title="CLASSES2:th.57">Th57</a></i>;<br/>
<a NAME="E4:74_1"/><b>then </b>
<font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="classes2.html#T80" target="_self" title="CLASSES2:th.80">Th80</a></i>;<br/>
<b>hence </b><a NAME="E5:74_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:74_1"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="ordinal1.html#T7" title="ORDINAL1:th.7">ORDINAL1:7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>assume </b><a NAME="E2:74"/><i><font color="Green" title="E53">A2</font></i>: 
 <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font></span><br/>

<b>assume </b><a NAME="E3:74"/>
not <font color="Maroon" title="c1">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:74"/><b>then </b>
<font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#T26" title="ORDINAL1:th.26">ORDINAL1:26</a></i>;<br/>
<a NAME="E5:74"/><b>then </b>
 <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="classes2.html#T80" target="_self" title="CLASSES2:th.80">Th80</a></i>;<br/>
<b>hence </b><a NAME="E6:74"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:74"><i><font color="Green" title="E53">A2</font></i></a>, <a class="ref" href="ordinal1.html#T7" title="ORDINAL1:th.7">ORDINAL1:7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
