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<b>let </b><font color="Maroon">Y1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y2</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:18_1_2"/><i><font color="Green">E36</font></i>: 
( ( 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> <font color="Maroon">Y1</font> iff  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> ) ) &amp; ( 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> <font color="Maroon">Y2</font> iff  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> ) ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_2_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/><a NAME="E1:18_1_2_1"/>
( ( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y1</font> implies  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> ) &amp; (  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> implies <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y1</font> ) &amp; ( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y2</font> implies  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> ) &amp; (  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> implies <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y2</font> ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:18_1_2_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y1</font> iff <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y2</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:18_1_2"/>
<font color="Maroon">Y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y2</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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