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<b>let </b><font color="Maroon">X</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="intpro_1.html#K1" target="_self">MC-wff</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="intpro_1.html#D22" target="_self">INTPRO_1:def 22</a><br/><b>let </b><font color="Maroon">q</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/><b>let </b><font color="Maroon">r</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/>







<b>thus </b><a NAME="E1:144"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>

<b>thus </b><a NAME="E2:144"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>

<b>thus </b><a NAME="E3:144"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>

<b>thus </b><a NAME="E4:144"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>

<b>thus </b><a NAME="E5:144"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>

<b>thus </b><a NAME="E6:144"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>

<b>thus </b><a NAME="E7:144"/>
<font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>

<b>thus </b><a NAME="E8:144"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>

<b>thus </b><a NAME="E9:144"/>
<a href="intpro_1.html#K2" target="_self">FALSUM</a>  <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>

<b>thus </b><a NAME="E10:144"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <a href="intpro_1.html#K2" target="_self">FALSUM</a> </span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>

<b>thus </b><a NAME="E11:144"/>
<span class="p1">(<span class="default"><a href="intpro_1.html#K6" target="_self">Nes</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="intpro_1.html#K6" target="_self">Nes</a> <font color="Maroon">p</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><a href="intpro_1.html#K6" target="_self">Nes</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T32" target="_self">Th32</a></i>;<br/>

<b>thus </b><a NAME="E12:144"/>
<span class="p1">(<span class="default"><a href="intpro_1.html#K6" target="_self">Nes</a> <font color="Maroon">p</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T33" target="_self">Th33</a></i>;<br/>

<b>thus </b><a NAME="E13:144"/>
<span class="p1">(<span class="default"><a href="intpro_1.html#K6" target="_self">Nes</a> <font color="Maroon">p</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><a href="intpro_1.html#K6" target="_self">Nes</a> <span class="p2">(<span class="default"><a href="intpro_1.html#K6" target="_self">Nes</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T34" target="_self">Th34</a></i>;<br/>

<b>thus </b><a NAME="E14:144"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font> &amp; <font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font> implies <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="intpro_1.html#T30" target="_self">Th30</a></i>;<br/>

<b>thus </b><a NAME="E15:144"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font> implies  <a href="intpro_1.html#K6" target="_self">Nes</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="intpro_1.html#T36" target="_self">Th36</a></i>;<br/>


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