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<span class="kw">let </span><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">G</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">H</font> or  not <font color="Maroon" title="c2">H</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">G</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:79"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<font color="Maroon" title="c1">G</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">H</font>
 <span class="kw">and </span><br/><a NAME="E2:79"/>
<font color="Maroon" title="c1">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">H</font>
 <span class="kw">and </span><br/><a NAME="E3:79"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
<font color="Maroon" title="c2">H</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">G</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="qc_lang2.html#D22" target="_self" title="QC_LANG2:def.22">QC_LANG2:def 22</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">thus </span><a NAME="E4:79"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E3:79"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="qc_lang2.html#T79" target="_self" title="QC_LANG2:th.79">Th79</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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