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

<b>assume </b><a NAME="E1:17"/><i><font color="Green">E17</font></i>: 
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SFX</font> holds <br/> ex <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Y</font> <a href="hidden.html#R2">in</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">X</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Y</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="setfam_1.html#D2" target="_self">SETFAM_1:def 2</a><br/>

<b>assume </b><a NAME="E2:17"/><i><font color="Green">E18</font></i>: 
not <font color="Maroon">SFX</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">SFX</font>;<br/>
<a NAME="E4:17"/>
 ex <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Y</font> <a href="hidden.html#R2">in</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Y</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:17"/>
contradiction
 ;<br/>


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