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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/>



<b>thus </b><a NAME="E1:91"/>
(  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c2">q</font> implies  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c2">q</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_1"/><i><font color="Green" title="E70">A1</font></i>: 
 <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c2">q</font>
 ;<br/>

<a NAME="E2:91_1"/>
 <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T67" target="_self" title="LUKASI_1:th.67">Th67</a></i>;<br/>
<b>hence </b><a NAME="E3:91_1"/>
 <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c2">q</font>
 <b>by </b><i><a class="txt" href="lukasi_1.html#E1:91_1"><i><font color="Green" title="E70">A1</font></i></a>, <a class="ref" href="cqc_the1.html#T104" title="CQC_THE1:th.104">CQC_THE1:104</a></i>;<br/>


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

<b>assume </b><a NAME="E2:91"/><i><font color="Green" title="E70">A2</font></i>: 
 <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c2">q</font>
 ;<br/>

<a NAME="E3:91"/>
 <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T65" target="_self" title="LUKASI_1:th.65">Th65</a></i>;<br/>
<b>hence </b><a NAME="E4:91"/>
 <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c2">q</font>
 <b>by </b><i><a class="txt" href="lukasi_1.html#E2:91"><i><font color="Green" title="E70">A2</font></i></a>, <a class="ref" href="lukasi_1.html#T43" target="_self" title="LUKASI_1:th.43">Th43</a></i>;<br/>


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