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

<span class="kw">thus </span><a NAME="E1:46"/>
(  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>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T16" target="_self" title="QC_LANG1:th.16">Th49</a>, <a class="ref" href="qc_lang1.html#T17" target="_self" title="QC_LANG1:th.17">Th50</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E2:46"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
( <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 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T16" target="_self" title="QC_LANG1:th.16">Th49</a></span>;<br/>
<a NAME="E3:46"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
( <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 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T16" target="_self" title="QC_LANG1:th.16">Th49</a></span>;<br/>
<a NAME="E4:46"/>
( <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 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T16" target="_self" title="QC_LANG1:th.16">Th49</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:46"/>
(  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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="qc_lang1.html#T17" target="_self" title="QC_LANG1:th.17">Th50</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
