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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <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="E1:8"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</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">X</font>;<br/>
<b>assume </b><a NAME="E3:8"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">X</font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E4:8"/><b>then </b>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:8"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> )
 
<b>by </b><i>, <a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E6:8"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 
<b>by </b><i>, , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<b>hence </b><a NAME="E7:8"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>


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