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



<b>assume </b><a NAME="E1:63"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>   st <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Z</font> &amp; <font color="Olive">Z</font> is <a href="ordinal1.html#V1">epsilon-transitive</a> holds <br/><font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Z</font>
 ;<br/>

<b>assume </b><a NAME="E2:63"/>
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> is <a href="ordinal1.html#V1">epsilon-transitive</a> )
 ;<br/>

<b>hence </b><a NAME="E3:63"/>
 <a href="classes1.html#K5" target="_self">the_transitive-closure_of</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<a NAME="E4:63"/>
(  <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> &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/>
<b>hence </b><a NAME="E5:63"/>
<font color="Maroon">Y</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/>;<br/>


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