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<b>let </b><font color="Maroon">F</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/><b>let </b><font color="Maroon">G</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/><b>let </b><font color="Maroon">H</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/>





<a NAME="E1:67"/>
( <font color="Maroon">F</font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">F</font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">G</font> &amp; <font color="Maroon">G</font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">F</font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">G</font> )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T24" target="_self">Th24</a></i>;<br/>
<b>hence </b><a NAME="E2:67"/>
( <font color="Maroon">F</font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">G</font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">H</font> implies ( <font color="Maroon">F</font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">H</font> &amp; <font color="Maroon">G</font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">H</font> ) )
 <b>by </b><i/>;<br/>


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