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

<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/>
<a NAME="E2:5_1_1"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="finsub_1.html#D5">FINSUB_1:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">s</font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="subset_1.html#T55">SUBSET_1:55</a></i>;<br/>
<b>take </b>
<font color="Maroon">s</font>
;<br/>

<b>thus </b><a NAME="E4:5_1_1"/>
not <font color="Maroon">s</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>assume </b><a NAME="E5:5_1_1"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">s</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="setfam_1.html#D9">SETFAM_1:def 9</a><br/>

<b>hence </b><a NAME="E6:5_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div>
