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<b>let </b><font color="Maroon">p1</font> be   <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K8" target="_self">PairSet</a> <font color="Maroon">X</font></span>)</span>, <font color="Maroon">p2</font> be   <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K8" target="_self">PairSet</a> <font color="Maroon">X</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:42_1_2"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">z</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">p1</font> iff  ex <font color="Olive">t</font> being   <a href="hidden.html#M1">set</a>  ex <font color="Olive">l</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">l</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> &amp; <font color="Olive">z</font> <a href="hidden.html#R1">=</a>  <a href="pencil_4.html#K9" target="_self">PairSet</a> <font color="Olive">t</font>,<font color="Olive">l</font> ) )
 <b>and </b><br/><a NAME="E2:42_1_2"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">z</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">p2</font> iff  ex <font color="Olive">t</font> being   <a href="hidden.html#M1">set</a>  ex <font color="Olive">l</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">l</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> &amp; <font color="Olive">z</font> <a href="hidden.html#R1">=</a>  <a href="pencil_4.html#K9" target="_self">PairSet</a> <font color="Olive">t</font>,<font color="Olive">l</font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:42_1_2_1"/>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">p1</font> iff  ex <font color="Olive">t</font> being   <a href="hidden.html#M1">set</a>  ex <font color="Olive">l</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">l</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="pencil_4.html#K9" target="_self">PairSet</a> <font color="Olive">t</font>,<font color="Olive">l</font> ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:42_1_2_1"/>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">p1</font> iff <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">p2</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:42_1_2"/>
<font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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