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<b>let </b><font color="Maroon" title="c1">H</font>, <font color="Maroon" title="c2">F</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> ;<br/><b>let </b><font color="Maroon" title="c3">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>;<br/>





<a NAME="E1:68"/>
<font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">H</font>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T91" target="_self" title="QC_LANG2:th.91">Th91</a></i>;<br/>
<b>hence </b><a NAME="E2:68"/>
(  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">F</font> implies <font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">F</font> )
 <b>by </b><i><a class="ref" href="qc_lang2.html#T83" target="_self" title="QC_LANG2:th.83">Th83</a></i>;<br/>


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