<?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">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>thus </b><a NAME="E1:7"/>
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> implies <span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">X</font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">Y</font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 ;<br/>

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:7_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">X</font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:7_1"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">y</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> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E5:7_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">Y</font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span>
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:7"/><i><font color="Green">E23</font></i>: 
<span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">X</font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">Y</font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span>
 ;<br/>

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:7"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E4:7"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="relset_2.html#NK1" target="_self">{_{</a><span class="default"><font color="Maroon">X</font></span><a href="relset_2.html#NK1" target="_self">}_}</a></span>
 
<b>by </b><i>, </i>;<br/>
<b>then consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:7"/><i><font color="Green">E26</font></i>: 
( <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 <b>by </b><i>, </i>;<br/>
<b>thus </b><a NAME="E7:7"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T6">ZFMISC_1:6</a></i>;<br/>


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