<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">H</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>thus </b><a NAME="E1:77"/>
(  not <font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a>  <a href="qc_lang2.html#K1" title="QC_LANG2:func.1">FALSUM</a>  or <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K1" title="QC_LANG2:func.1">FALSUM</a>  or <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:77_1"/>
( <font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a>  <a href="qc_lang2.html#K1" title="QC_LANG2:func.1">FALSUM</a>  &amp; <font color="Maroon" title="c1">H</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="qc_lang2.html#K1" title="QC_LANG2:func.1">FALSUM</a>  )
 ;<br/>

<a NAME="E2:77_1"/><b>then </b>
<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_lang2.html#K1" title="QC_LANG2:func.1">FALSUM</a> 
 
<b>by </b><i><a class="ref" href="qc_lang2.html#D22" target="_self" title="QC_LANG2:def.22">Def22</a></i>;<br/>
<a NAME="E3:77_1"/><b>then </b>
<font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> 
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T86" target="_self" title="QC_LANG2:th.86">Th86</a></i>;<br/>
<b>hence </b><a NAME="E4:77_1"/>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> 
 <b>by </b><i><a class="ref" href="qc_lang2.html#T99" target="_self" title="QC_LANG2:th.99">Th99</a></i>;<br/>


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

<a NAME="E2:77"/>
 <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a>  <a href="qc_lang2.html#K1" title="QC_LANG2:func.1">FALSUM</a> 
 
<b>by </b><i><a class="ref" href="qc_lang2.html#D20" target="_self" title="QC_LANG2:def.20">Def20</a></i>;<br/>
<a NAME="E3:77"/><b>then </b>
 <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a>  <a href="qc_lang2.html#K1" title="QC_LANG2:func.1">FALSUM</a> 
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T73" target="_self" title="QC_LANG2:th.73">Th73</a></i>;<br/>
<b>hence </b><a NAME="E4:77"/>
( ( <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K1" title="QC_LANG2:func.1">FALSUM</a>  or <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  ) implies <font color="Maroon" title="c1">H</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a>  <a href="qc_lang2.html#K1" title="QC_LANG2:func.1">FALSUM</a>  )
 <b>by </b><i><a class="ref" href="qc_lang2.html#D22" target="_self" title="QC_LANG2:def.22">Def22</a></i>;<br/>


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