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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a>;<br/>

<a NAME="E1:32"/>
<font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#D2" title="QC_LANG2:def.2">QC_LANG2:def 2</a></i>;<br/>
<a NAME="E2:32"/><b>then </b>
( ( <font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> implies <font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> ) &amp; ( <font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> implies <font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> ) &amp; ( <font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> implies ( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> &amp;  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> ) ) &amp; ( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> &amp;  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> implies <font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> ) &amp; (  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> implies <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> ) &amp; ( <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> implies  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> ) )
 
<b>by </b><i><a class="ref" href="qc_lang3.html#T25" target="_self" title="QC_LANG3:th.25">Th25</a>, <a class="ref" href="qc_lang3.html#T26" target="_self" title="QC_LANG3:th.26">Th26</a></i>;<br/>
<b>hence </b><a NAME="E3:32"/>
( ( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> ) iff <font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Maroon" title="c2">q</font> is <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a> )
 ;<br/>


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