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

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



<b>assume </b><a NAME="E1:31"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:31_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">X</font></span>)</span>,<font color="Maroon">x</font>
 ;<br/><a NAME="E2:31_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:31_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/></div><b>end;</b></div>
<a NAME="E3:31"/><b>then </b>
for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">X</font></span>)</span>,<font color="Maroon">x</font> iff <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:31"/>
 <a href="eqrel_1.html#K7" target="_self">Class</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">X</font></span>)</span>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div>
