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

<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <a href="xboole_0.html#K1">{}</a>  <a href="relat_1.html#K10" target="_self">"</a> <font color="Maroon">Y</font>;<br/>
<b>assume </b><a NAME="E2:162"/>
not <a href="xboole_0.html#K1">{}</a>  <a href="relat_1.html#K10" target="_self">"</a> <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E3:162"/><b>then </b>
 ex <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:162"/>
contradiction
 ;<br/>


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