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



<b>assume </b><a NAME="E1:1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<b>assume </b><a NAME="E2:1"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds  <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>thus </b><a NAME="E1:1_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> implies <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>by </b><i/>;<br/><b>assume </b><a NAME="E2:1_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><b>consider </b><font color="Maroon">a0</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/><a NAME="E4:1_1"/>
<font color="Maroon">a0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E5:1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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