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<span class="kw">consider </span><font color="Maroon" title="c2">x</font> being   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>, <font color="Maroon" title="c3">F1</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a><span class="kw"> such that </span><br/><a NAME="E2:22_1_1"/><span class="lab"><font color="Green" title="E23">A2</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">F1</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="qc_lang2.html#D13" title="QC_LANG2:def.13">QC_LANG2:def 13</a></span>;<br/>
<a NAME="E3:22_1_1"/>
<font color="Maroon" title="c1">p</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"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c3">F1</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="ref" href="qc_lang2.html#D5" title="QC_LANG2:def.5">QC_LANG2:def 5</a></span>;<br/>
<a NAME="E4:22_1_1"/><span class="kw">then </span>
 <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c3">F1</font></span>)</span>) is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_lang.html#T8" title="CQC_LANG:th.8">CQC_LANG:8</a></span>;<br/>
<a NAME="E5:22_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A3</font></span>: 
 <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <font color="Maroon" title="c3">F1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_lang.html#T13" title="CQC_LANG:th.13">CQC_LANG:13</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">F1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">F1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a>  &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> st <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">F1</font>) )</span><br/>

<span class="kw">thus </span><a NAME="E6:22_1_1"/>
( <font color="Maroon" title="c3">F1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a>  &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> st <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">F1</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="txt" href="#E5:22_1_1"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="ref" href="cqc_lang.html#T8" title="CQC_LANG:th.8">CQC_LANG:8</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/>


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