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<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">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>assume </b><a NAME="E1:62"/><i><font color="Green" title="E44">A1</font></i>: 
( ( <font color="Maroon" title="c1">F</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font> ) or ( <font color="Maroon" title="c1">F</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c3">H</font> ) or ( <font color="Maroon" title="c1">F</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c3">H</font> ) or ( <font color="Maroon" title="c1">F</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font> ) or ( <font color="Maroon" title="c1">F</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c3">H</font> ) or ( <font color="Maroon" title="c1">F</font> <a href="qc_lang2.html#R1" title="QC_LANG2:pred.1">is_immediate_constituent_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c3">H</font> ) )
 ;<br/>

<a NAME="E2:62"/><b>then </b>
( <font color="Maroon" title="c1">F</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c2">G</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font> )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#D22" target="_self" title="QC_LANG2:def.22">Def22</a>, <a class="ref" href="qc_lang2.html#T72" target="_self" title="QC_LANG2:th.72">Th72</a></i>;<br/>
<b>hence </b><a NAME="E3:62"/>
<font color="Maroon" title="c1">F</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="ref" href="qc_lang2.html#T77" target="_self" title="QC_LANG2:th.77">Th77</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="qc_lang2.html#D22" target="_self" title="QC_LANG2:def.22">QC_LANG2:def 22</a><br/>

<b>thus </b><a NAME="E4:62"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="txt" href="qc_lang2.html#E1:62"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="qc_lang2.html#T79" target="_self" title="QC_LANG2:th.79">Th79</a>, <a class="ref" href="qc_lang2.html#T81" target="_self" title="QC_LANG2:th.81">Th81</a>, <a class="ref" href="qc_lang2.html#T82" target="_self" title="QC_LANG2:th.82">Th82</a></i>;<br/>


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