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<b>thus </b><a NAME="E1:45"/>
( not  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> &amp; not  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> &amp; not  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> &amp; not  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> )
 <b>by </b><i><a class="ref" href="qc_lang1.html#T49" target="_self" title="QC_LANG1:th.49">Th49</a>, <a class="ref" href="qc_lang1.html#T50" target="_self" title="QC_LANG1:th.50">Th50</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>  holds <br/> ( not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> &amp; <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> &amp; <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> &amp; <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> &amp; <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> &amp; <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> &amp; <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> ) )</span><br/>

<b>let </b><font color="Maroon" title="c1">p</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> ) )</span><br/>

<a NAME="E2:45"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; ( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) &amp; ( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 ) )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#T49" target="_self" title="QC_LANG1:th.49">Th49</a></i>;<br/>
<b>hence </b><a NAME="E3:45"/>
( not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> &amp; <font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> ) )
 <b>by </b><i><a class="ref" href="qc_lang1.html#T50" target="_self" title="QC_LANG1:th.50">Th50</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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