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<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/>

<b>thus </b><a NAME="E1:78"/>
(  not <font color="Maroon">H</font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a>  or <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a>  or <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K11">VERUM</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:78_1"/>
( <font color="Maroon">H</font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a>  &amp; <font color="Maroon">H</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a>  )
 ;<br/>

<a NAME="E2:78_1"/><b>then </b>
<font color="Maroon">H</font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a> 
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E3:78_1"/><b>then </b>
<font color="Maroon">H</font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a>  <a href="qc_lang1.html#K11">VERUM</a> 
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E4:78_1"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K11">VERUM</a> 
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>

<a NAME="E2:78"/>
 <a href="qc_lang1.html#K11">VERUM</a>  <a href="qc_lang2.html#R1" target="_self">is_immediate_constituent_of</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:78"/><b>then </b>
 <a href="qc_lang1.html#K11">VERUM</a>  <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:78"/>
( ( <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a>  or <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K11">VERUM</a>  ) implies <font color="Maroon">H</font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a>  <a href="qc_lang2.html#K1" target="_self">FALSUM</a>  )
 <b>by </b><i><a class="ref" href="qc_lang2.html#T4" target="_self">Th4</a></i>;<br/>


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