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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>thus </b><a NAME="E1:76"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> implies  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">c<sub>2</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:76_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:76_1"/>
not  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:76_1"/><b>then </b>
 <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="classes2.html#T57" target="_self">Th57</a></i>;<br/>
<a NAME="E4:76_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="classes2.html#T80" target="_self">Th80</a></i>;<br/>
<b>hence </b><a NAME="E5:76_1"/>
contradiction
 <b>by </b><i><a class="txt" href="classes2.html#E1:76_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="ordinal1.html#T7">ORDINAL1:7</a></i>;<br/>


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

<b>assume </b><a NAME="E2:76"/><i><font color="Green">E52</font></i>: 
 <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>assume </b><a NAME="E3:76"/>
not <font color="Maroon">c<sub>1</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E4:76"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#T26">ORDINAL1:26</a></i>;<br/>
<a NAME="E5:76"/><b>then </b>
 <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="classes2.html#T80" target="_self">Th80</a></i>;<br/>
<b>hence </b><a NAME="E6:76"/>
contradiction
 <b>by </b><i><a class="txt" href="classes2.html#E2:76"><i><font color="Green">E52</font></i></a>, <a class="ref" href="ordinal1.html#T7">ORDINAL1:7</a></i>;<br/>


</div>
