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<b>let </b><font color="Maroon">X1</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Maroon">X2</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>

<b>assume </b><a NAME="E1:3_2_2"/><i><font color="Green">E26</font></i>: 
( ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">x</font> is <a href="finset_1.html#V1">finite</a> ) ) ) &amp; ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X2</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">x</font> is <a href="finset_1.html#V1">finite</a> ) ) ) &amp; not <font color="Maroon">X1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X2</font> )
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:3_2_2"/><i><font color="Green">E27</font></i>: 
( ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X2</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X2</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font> ) )
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<a NAME="E4:3_2_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X2</font> iff (  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> or  not <font color="Maroon">x</font> is <a href="finset_1.html#V1">finite</a> ) )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:3_2_2"/>
contradiction
 <b>by </b><i/>;<br/>


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