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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">B</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">X</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>thus </b><a NAME="E1:76_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setwiseo.html#K10" target="_self">FinUnion</a> <font color="Maroon">B</font>,<span class="p1">(<span class="default"><a href="setwiseo.html#K11" target="_self">singleton</a> <font color="Maroon">X</font></span>)</span> implies <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:76_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setwiseo.html#K10" target="_self">FinUnion</a> <font color="Maroon">B</font>,<span class="p1">(<span class="default"><a href="setwiseo.html#K11" target="_self">singleton</a> <font color="Maroon">X</font></span>)</span>
 ;<br/>

<a NAME="E2:76_1_1"/><b>then </b>
 ex <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setwiseo.html#K11" target="_self">singleton</a> <font color="Maroon">X</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">i</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:76_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div><b>assume </b><a NAME="E2:76_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/><b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font> <b>by </b><i/>;<br/><a NAME="E4:76_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setwiseo.html#K11" target="_self">singleton</a> <font color="Maroon">X</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x'</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E5:76_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setwiseo.html#K10" target="_self">FinUnion</a> <font color="Maroon">B</font>,<span class="p1">(<span class="default"><a href="setwiseo.html#K11" target="_self">singleton</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:76"/>
 <a href="setwiseo.html#K10" target="_self">FinUnion</a> <font color="Maroon">B</font>,<span class="p1">(<span class="default"><a href="setwiseo.html#K11" target="_self">singleton</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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