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<span class="kw">let </span><font color="Maroon" title="c1">p</font> be    <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> ; <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">x</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a>  holds  <font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a>  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ; <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="c1">p</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a>  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font>)</span><br/>



<a NAME="E1:15"/>
<font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a>  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#T71" title="QC_LANG2:th.71">QC_LANG2:71</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:15"/>
<font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a>  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#D21" title="QC_LANG2:def.21">QC_LANG2:def 21</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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