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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</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/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:58_1"/><i><font color="Green" title="E42">A1</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font> <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> 
 ;<br/><a NAME="E2:58_1"/>
( <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="c2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c1">p</font> <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>  &amp; <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="c2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">q</font> <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#D14" target="_self" title="INTPRO_1:def.14">Def14</a></i>;<br/><b>hence </b><a NAME="E3:58_1"/>
( <font color="Maroon" title="c1">p</font> <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>  &amp; <font color="Maroon" title="c2">q</font> <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#E1:58_1"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="intpro_1.html#D14" target="_self" title="INTPRO_1:def.14">Def14</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:58"/><i><font color="Green" title="E42">A2</font></i>: 
( <font color="Maroon" title="c1">p</font> <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>  &amp; <font color="Maroon" title="c2">q</font> <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>  )
 ;<br/>

<a NAME="E3:58"/>
<font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <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="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#D14" target="_self" title="INTPRO_1:def.14">Def14</a></i>;<br/>
<a NAME="E4:58"/><b>then </b>
<font color="Maroon" title="c2">q</font> <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="c2">q</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="txt" href="intpro_1.html#E2:58"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="intpro_1.html#D14" target="_self" title="INTPRO_1:def.14">Def14</a></i>;<br/>
<b>hence </b><a NAME="E5:58"/>
<font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font> <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#E2:58"><i><font color="Green" title="E42">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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