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

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1"><b>now </b></a><div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:2_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E2:2_1"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>   holds <br/>(  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> or  not <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> or  not <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 ;<br/><b>consider </b><font color="Maroon">p</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/><a NAME="E4:2_1"/>
for <font color="Olive">z</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff <font color="Olive">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E5:2_1"/><b>then </b>
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">p</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:2_1"/>
 ex <font color="Olive">a</font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">a</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:2"/>
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or  ex <font color="Olive">a</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">a</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> ) ) )
 ;<br/>


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