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<b>let </b><font color="Maroon" title="c1">P</font>, <font color="Maroon" title="c2">Q</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:78"/>
<font color="Maroon" title="c1">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Q</font>
 ;<br/>

<a NAME="E2:78"/><b>then </b><i><font color="Green" title="E31">A1</font></i>: 
<font color="Maroon" title="c2">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">Q</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c1">P</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></i>;<br/>
<b>assume </b><a NAME="E3:78"/><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c1">P</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">Q</font>
 ;<br/>

<b>assume </b><a NAME="E4:78"/>
<font color="Maroon" title="c2">Q</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>hence </b><a NAME="E5:78"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_2.html#E2:78"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="tex_2.html#E3:78"><i><font color="Green" title="E32">A2</font></i></a></i>;<br/>


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