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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/>





<a NAME="E1:63"/><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="ref" href="intpro_1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E2:63"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></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">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="ref" href="intpro_1.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E3:63"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="txt" href="intpro_1.html#E1:63"><i><font color="Green">E44</font></i></a>, <a class="ref" href="intpro_1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E4:63"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <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">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="ref" href="intpro_1.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E5:63"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <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">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></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">c<sub>1</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="ref" href="intpro_1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E6:63"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <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">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="txt" href="intpro_1.html#E4:63"><i><font color="Green">E45</font></i></a>, <a class="ref" href="intpro_1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E7:63"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <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">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="ref" href="intpro_1.html#T29" target="_self">Th29</a></i>;<br/>
<a NAME="E8:63"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="txt" href="intpro_1.html#E6:63"><i><font color="Green">E46</font></i></a>, <a class="ref" href="intpro_1.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E9:63"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="ref" href="intpro_1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E10:63"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="ref" href="intpro_1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E11:63"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 
<b>by </b><i><a class="txt" href="intpro_1.html#E9:63"><i><font color="Green">E48</font></i></a>, <a class="ref" href="intpro_1.html#T32" target="_self">Th32</a></i>;<br/>
<b>hence </b><a NAME="E12:63"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K8" target="_self">IPC-Taut</a> 
 <b>by </b><i><a class="txt" href="intpro_1.html#E8:63"><i><font color="Green">E47</font></i></a>, <a class="ref" href="intpro_1.html#T26" target="_self">Th26</a></i>;<br/>


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