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

<b>assume </b><a NAME="E1:34"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E2:34"/>
 <a href="classes1.html#K1">Tarski-Class</a> <span class="p1">(<span class="default"><a href="classes1.html#K5">the_transitive-closure_of</a> <font color="Maroon">Y</font></span>)</span> <a href="classes1.html#R1">is_Tarski-Class_of</a>  <a href="classes1.html#K5">the_transitive-closure_of</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="classes1.html#D4">CLASSES1:def 4</a></i>;<br/>
<a NAME="E3:34"/><b>then </b><i><font color="Green">E28</font></i>: 
 <a href="classes1.html#K5">the_transitive-closure_of</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1">Tarski-Class</a> <span class="p1">(<span class="default"><a href="classes1.html#K5">the_transitive-closure_of</a> <font color="Maroon">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="classes1.html#D3">CLASSES1:def 3</a></i>;<br/>
<a NAME="E4:34"/>
<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K5">the_transitive-closure_of</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="classes1.html#T59">CLASSES1:59</a></i>;<br/>
<a NAME="E5:34"/><b>then </b>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K5">the_transitive-closure_of</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E6:34"/><b>then </b>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1">Tarski-Class</a> <span class="p1">(<span class="default"><a href="classes1.html#K5">the_transitive-closure_of</a> <font color="Maroon">Y</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:34"/>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K2">the_universe_of</a> <font color="Maroon">Y</font>
 ;<br/>


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