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<b>let </b><font color="Maroon">c<sub>1</sub></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="E1:76"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a>  <a href="qc_lang1.html#K11">VERUM</a>  implies <font color="Maroon">c<sub>1</sub></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="76_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:76_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a>  <a href="qc_lang1.html#K11">VERUM</a> 
 ;<br/>

<b>assume </b><a NAME="E2:76_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="qc_lang1.html#K11">VERUM</a> 
 ;<br/>

<a NAME="E3:76_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a>  <a href="qc_lang1.html#K11">VERUM</a> 
 
<b>by </b><i><a class="txt" href="qc_lang2.html#E1:76_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="qc_lang2.html#D22" target="_self">Def22</a></i>;<br/>
<b>hence </b><a NAME="E4:76_1"/>
contradiction
 <b>by </b><i><a class="ref" href="qc_lang2.html#T58" target="_self">Th58</a>, <a class="ref" href="qc_lang2.html#T75" target="_self">Th75</a></i>;<br/>


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

<b>thus </b><a NAME="E2:76"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K11">VERUM</a>  implies <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a>  <a href="qc_lang1.html#K11">VERUM</a>  )
 ;<br/>


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