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<b>let </b><font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">P</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>;<br/>





<b>consider </b><font color="Maroon">R</font> being   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">Y</font><b> such that </b><br/><a NAME="E2:15"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T43">EQREL_1:43</a></i>;<br/>
<b>take </b>
 <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<font color="Maroon">y</font>
;<br/>

<b>thus </b><a NAME="E3:15"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T28">EQREL_1:28</a></i>;<br/>

<b>thus </b><a NAME="E4:15"/>
 <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 <b>by </b><i>, <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/>


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