<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">s</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <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#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</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> </span><br/>





<b>set </b><font color="Maroon" title="c4">P</font> = <font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font>;<br/>
<b>set </b><font color="Maroon" title="c5">Q</font> = <font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font>;<br/>
<a NAME="E1:104"/>
<font color="Maroon" title="c3">s</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#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</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="ref" href="intpro_1.html#D14" target="_self" title="INTPRO_1:def.14">Def14</a></i>;<br/>
<a NAME="E2:104"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span> <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#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</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#T63" target="_self" title="INTPRO_1:th.63">Th63</a></i>;<br/>
<a NAME="E3:104"/><b>then </b><i><font color="Green" title="E79">A1</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <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#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></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#T63" target="_self" title="INTPRO_1:th.63">Th63</a></i>;<br/>
<a NAME="E4:104"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></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">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c1">p</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="ref" href="intpro_1.html#T56" target="_self" title="INTPRO_1:th.56">Th56</a></i>;<br/>
<a NAME="E5:104"/><b>then </b><i><font color="Green" title="E80">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</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">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c1">p</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="#E3:104"><i><font color="Green" title="E79">A1</font></i></a>, <a class="ref" href="intpro_1.html#T26" target="_self" title="INTPRO_1:th.26">Th26</a></i>;<br/>
<a NAME="E6:104"/><i><font color="Green" title="E81">A3</font></i>: 
<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="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</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="ref" href="intpro_1.html#D14" target="_self" title="INTPRO_1:def.14">Def14</a></i>;<br/>
<a NAME="E7:104"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span> <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#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</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="E8:104"/><b>then </b>
<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#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</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="txt" href="#E6:104"><i><font color="Green" title="E81">A3</font></i></a>, <a class="ref" href="intpro_1.html#T26" target="_self" title="INTPRO_1:th.26">Th26</a></i>;<br/>
<a NAME="E9:104"/><b>then </b><i><font color="Green" title="E82">A4</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c1">p</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="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></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#T63" target="_self" title="INTPRO_1:th.63">Th63</a></i>;<br/>
<a NAME="E10:104"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span></span>)</span> <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#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</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#T54" target="_self" title="INTPRO_1:th.54">Th54</a></i>;<br/>
<a NAME="E11:104"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c1">p</font></span>)</span> <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#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</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="txt" href="#E9:104"><i><font color="Green" title="E82">A4</font></i></a>, <a class="ref" href="intpro_1.html#T26" target="_self" title="INTPRO_1:th.26">Th26</a></i>;<br/>
<b>hence </b><a NAME="E12:104"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <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#K5" title="INTPRO_1:func.5">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">s</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="txt" href="#E5:104"><i><font color="Green" title="E80">A2</font></i></a>, <a class="ref" href="intpro_1.html#T26" target="_self" title="INTPRO_1:th.26">Th26</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
