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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>; <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  <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">p</font>)</span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">p</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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"> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">p</font>)</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">q</font> =  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">p</font>);<br/>
<a NAME="E1:49"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
 <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">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="ref" href="qc_lang1.html#D19" title="QC_LANG1:def.19">QC_LANG1:def 19</a></span>;<br/>
<a NAME="E2:49"/><span class="kw">then </span>
 <a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D25" title="QC_LANG1:def.25">QC_LANG1:def 25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:49"/>
<span class="p1">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">p</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="cqc_lang.html#T22" target="_self" title="CQC_LANG:th.22">Th35</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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