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

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

<a NAME="E1:69"/>
 <a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">X</font> is <a href="ordinal1.html#V1">epsilon-transitive</a>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">A</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E3:69"/><i><font color="Green">E25</font></i>: 
 <a href="classes1.html#K1" target="_self">Tarski-Class</a> <span class="p1">(<span class="default"><a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">X</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K4" target="_self">Rank</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<a NAME="E4:69"/>
(  <a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <span class="p1">(<span class="default"><a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">X</font></span>)</span> &amp; <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">X</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:69"/><b>then </b>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <span class="p1">(<span class="default"><a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">X</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E6:69"/><b>then </b>
( <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K4" target="_self">Rank</a> <font color="Maroon">A</font> &amp;  <a href="classes1.html#K4" target="_self">Rank</a> <font color="Maroon">A</font> is <a href="ordinal1.html#V1">epsilon-transitive</a> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:69"/>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K4" target="_self">Rank</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/>


</div>
