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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a> ;<br/>





<b>set </b><font color="Maroon" title="c4">P</font> = <font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">q</font>;<br/>
<b>set </b><font color="Maroon" title="c5">Q</font> = <font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">s</font>;<br/>
<b>set </b><font color="Maroon" title="c6">S</font> = <font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font>;<br/>
<b>set </b><font color="Maroon" title="c7">T</font> = <font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c1">p</font>;<br/>
<a NAME="E1:75"/><i><font color="Green" title="E54">A1</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K8" title="INTPRO_1:func.8">IPC-Taut</a> 
 
<b>by </b><i><a class="ref" href="intpro_1.html#T27" target="_self" title="INTPRO_1:th.27">Th27</a></i>;<br/>
<a NAME="E2:75"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K8" title="INTPRO_1:func.8">IPC-Taut</a> 
 
<b>by </b><i><a class="ref" href="intpro_1.html#T48" target="_self" title="INTPRO_1:th.48">Th48</a></i>;<br/>
<a NAME="E3:75"/><b>then </b><i><font color="Green" title="E55">A2</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K8" title="INTPRO_1:func.8">IPC-Taut</a> 
 
<b>by </b><i><a class="txt" href="intpro_1.html#E1:75"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="intpro_1.html#D14" target="_self" title="INTPRO_1:def.14">Def14</a></i>;<br/>
<a NAME="E4:75"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K8" title="INTPRO_1:func.8">IPC-Taut</a> 
 
<b>by </b><i><a class="ref" href="intpro_1.html#T46" target="_self" title="INTPRO_1:th.46">Th46</a></i>;<br/>
<b>hence </b><a NAME="E5:75"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K8" title="INTPRO_1:func.8">IPC-Taut</a> 
 <b>by </b><i><a class="txt" href="intpro_1.html#E3:75"><i><font color="Green" title="E55">A2</font></i></a>, <a class="ref" href="intpro_1.html#D14" target="_self" title="INTPRO_1:def.14">Def14</a></i>;<br/>


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