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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>thus </b><a NAME="E1:70"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">F</font> <a href="qc_lang1.html#K13">'&amp;'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">F</font> <a href="qc_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="qc_lang2.html#T23" target="_self">Th23</a></i>;<br/>

<a NAME="E2:70"/>
( <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> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span> &amp;  <a href="qc_lang1.html#K12">'not'</a> <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> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T24" target="_self">Th24</a></i>;<br/>
<b>hence </b><a NAME="E3:70"/><i><font color="Green">E29</font></i>: 
( <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_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">G</font> &amp;  <a href="qc_lang1.html#K12">'not'</a> <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_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">G</font> )
 <b>by </b><i>, <a class="ref" href="qc_lang2.html#T17" target="_self">Th17</a></i>;<br/>

<a NAME="E4:70"/>
<font color="Maroon">G</font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a>  <a href="qc_lang1.html#K12">'not'</a> <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E5:70"/>
<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_lang2.html#K2" target="_self">=&gt;</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="qc_lang2.html#T17" target="_self">Th17</a></i>;<br/>


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