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<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">q</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">X</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>





<b>thus </b><a NAME="E1:112"/>
( <font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font> implies <font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="112_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:112_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font>
 ;<br/>

<a NAME="E2:112_1"/>
 <a href="cqc_the1.html#NR5" target="_self">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T43" target="_self">Th43</a></i>;<br/>
<a NAME="E3:112_1"/><b>then </b>
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the1.html#T98">CQC_THE1:98</a></i>;<br/>
<b>hence </b><a NAME="E4:112_1"/>
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="lukasi_1.html#T54" target="_self">Th54</a>, <a class="ref" href="cqc_the1.html#T92">CQC_THE1:92</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:112"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font>
 ;<br/>

<a NAME="E3:112"/>
 <a href="cqc_the1.html#NR5" target="_self">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T41" target="_self">Th41</a></i>;<br/>
<a NAME="E4:112"/><b>then </b>
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="cqc_the1.html#T98">CQC_THE1:98</a></i>;<br/>
<b>hence </b><a NAME="E5:112"/>
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="lukasi_1.html#T54" target="_self">Th54</a>, <a class="ref" href="lukasi_1.html#T48" target="_self">Th48</a></i>;<br/>


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