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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="intpro_1.html#D19" target="_self" title="INTPRO_1:def.19">INTPRO_1:def 19</a><br/><b>let </b><font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</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>thus </b><a NAME="E1:119"/>
<font color="Maroon" title="c2">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="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T69" target="_self" title="INTPRO_1:th.69">Th69</a></i>;<br/>

<b>thus </b><a NAME="E2:119"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</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="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</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="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T69" target="_self" title="INTPRO_1:th.69">Th69</a></i>;<br/>

<b>thus </b><a NAME="E3:119"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T69" target="_self" title="INTPRO_1:th.69">Th69</a></i>;<br/>

<b>thus </b><a NAME="E4:119"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T69" target="_self" title="INTPRO_1:th.69">Th69</a></i>;<br/>

<b>thus </b><a NAME="E5:119"/>
<font color="Maroon" title="c2">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="c3">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="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T69" target="_self" title="INTPRO_1:th.69">Th69</a></i>;<br/>

<b>thus </b><a NAME="E6:119"/>
<font color="Maroon" title="c2">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">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T69" target="_self" title="INTPRO_1:th.69">Th69</a></i>;<br/>

<b>thus </b><a NAME="E7:119"/>
<font color="Maroon" title="c3">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="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T69" target="_self" title="INTPRO_1:th.69">Th69</a></i>;<br/>

<b>thus </b><a NAME="E8:119"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</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">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</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="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T69" target="_self" title="INTPRO_1:th.69">Th69</a></i>;<br/>

<b>thus </b><a NAME="E9:119"/>
<a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T69" target="_self" title="INTPRO_1:th.69">Th69</a></i>;<br/>

<b>thus </b><a NAME="E10:119"/>
<font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T69" target="_self" title="INTPRO_1:th.69">Th69</a></i>;<br/>

<b>thus </b><a NAME="E11:119"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="ref" href="intpro_1.html#T70" target="_self" title="INTPRO_1:th.70">Th70</a></i>;<br/>


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