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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#D22" target="_self" title="INTPRO_1:def.22">INTPRO_1:def 22</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="E1:142"/>
<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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T82" target="_self" title="INTPRO_1:th.82">Th82</a></i>;<br/>

<b>thus </b><a NAME="E2:142"/>
<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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T82" target="_self" title="INTPRO_1:th.82">Th82</a></i>;<br/>

<b>thus </b><a NAME="E3:142"/>
<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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T82" target="_self" title="INTPRO_1:th.82">Th82</a></i>;<br/>

<b>thus </b><a NAME="E4:142"/>
<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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T82" target="_self" title="INTPRO_1:th.82">Th82</a></i>;<br/>

<b>thus </b><a NAME="E5:142"/>
<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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T82" target="_self" title="INTPRO_1:th.82">Th82</a></i>;<br/>

<b>thus </b><a NAME="E6:142"/>
<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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T82" target="_self" title="INTPRO_1:th.82">Th82</a></i>;<br/>

<b>thus </b><a NAME="E7:142"/>
<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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T82" target="_self" title="INTPRO_1:th.82">Th82</a></i>;<br/>

<b>thus </b><a NAME="E8:142"/>
<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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T82" target="_self" title="INTPRO_1:th.82">Th82</a></i>;<br/>

<b>thus </b><a NAME="E9:142"/>
<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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T82" target="_self" title="INTPRO_1:th.82">Th82</a></i>;<br/>

<b>thus </b><a NAME="E10:142"/>
<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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T82" target="_self" title="INTPRO_1:th.82">Th82</a></i>;<br/>

<b>thus </b><a NAME="E11:142"/>
<span class="p1">(<span class="default"><a href="intpro_1.html#K6" title="INTPRO_1:func.6">Nes</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="c3">q</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"><a href="intpro_1.html#K6" title="INTPRO_1:func.6">Nes</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><a href="intpro_1.html#K6" title="INTPRO_1:func.6">Nes</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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T84" target="_self" title="INTPRO_1:th.84">Th84</a></i>;<br/>

<b>thus </b><a NAME="E12:142"/>
<span class="p1">(<span class="default"><a href="intpro_1.html#K6" title="INTPRO_1:func.6">Nes</a> <font color="Maroon" title="c2">p</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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T85" target="_self" title="INTPRO_1:th.85">Th85</a></i>;<br/>

<b>thus </b><a NAME="E13:142"/>
<span class="p1">(<span class="default"><a href="intpro_1.html#K6" title="INTPRO_1:func.6">Nes</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="intpro_1.html#K6" title="INTPRO_1:func.6">Nes</a> <span class="p2">(<span class="default"><a href="intpro_1.html#K6" title="INTPRO_1:func.6">Nes</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T86" target="_self" title="INTPRO_1:th.86">Th86</a></i>;<br/>

<b>thus </b><a NAME="E14:142"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K13" title="INTPRO_1:func.13">CnS4</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#K13" title="INTPRO_1:func.13">CnS4</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#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="ref" href="intpro_1.html#T83" target="_self" title="INTPRO_1:th.83">Th83</a></i>;<br/>

<b>thus </b><a NAME="E15:142"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font> implies  <a href="intpro_1.html#K6" title="INTPRO_1:func.6">Nes</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K13" title="INTPRO_1:func.13">CnS4</a> <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="ref" href="intpro_1.html#T87" target="_self" title="INTPRO_1:th.87">Th87</a></i>;<br/>


</div>
