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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> is <a href="ordinal1.html#V1">epsilon-transitive</a>
 
<b>by </b><i><a class="ref" href="classes1.html#T58" target="_self">Th58</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E3:69"/><i><font color="Green">E51</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">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K4" target="_self">Rank</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="classes1.html#T53" target="_self">Th53</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<a NAME="E4:69"/>
(  <a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> &amp; <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>1</sub></font> )
 
<b>by </b><i><a class="ref" href="classes1.html#T5" target="_self">Th5</a>, <a class="ref" href="classes1.html#T59" target="_self">Th59</a></i>;<br/>
<a NAME="E5:69"/><b>then </b>
<font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="classes1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E6:69"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K4" target="_self">Rank</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="classes1.html#K4" target="_self">Rank</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#E3:69"><i><font color="Green">E51</font></i></a>, <a class="ref" href="classes1.html#T37" target="_self">Th37</a></i>;<br/>
<b>hence </b><a NAME="E7:69"/>
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K4" target="_self">Rank</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/>


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