<?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="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:65"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:65"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="classes1.html#T59" target="_self">Th59</a></i>;<br/>
<a NAME="E3:65"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">c<sub>2</sub></font> is <a href="ordinal1.html#V1">epsilon-transitive</a> )
 
<b>by </b><i><a class="txt" href="classes1.html#E1:65"><i><font color="Green">E50</font></i></a>, <a class="ref" href="classes1.html#T58" target="_self">Th58</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:65"/>
 <a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="classes1.html#T60" target="_self">Th60</a></i>;<br/>


</div>
