<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">EqR</font> be   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c2">X</font>;<br/>





<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon" title="c3">EqR</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">x</font> = <font color="Maroon" title="c1">x</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font> ;<br/>
<b>consider </b><font color="Maroon" title="c5">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:43"/><i><font color="Green" title="E26">A2</font></i>: 
( <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c3">EqR</font>,<font color="Maroon" title="c5">y</font> )
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:43"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="eqrel_1.html#D5" target="_self" title="EQREL_1:def.5">Def5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">y</font> = <font color="Maroon" title="c5">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X</font> <b>by </b><i><a class="txt" href="eqrel_1.html#E4:43"><i><font color="Green" title="E26">A2</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">y</font>
;<br/>

<b>thus </b><a NAME="E6:43"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c3">EqR</font>,<font color="Maroon" title="c6">y</font>
 <b>by </b><i><a class="txt" href="eqrel_1.html#E4:43"><i><font color="Green" title="E26">A2</font></i></a></i>;<br/>


</div>
