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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/>





<a NAME="E1:67"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T89" target="_self">Th89</a></i>;<br/>
<b>hence </b><a NAME="E2:67"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang1.html#K13">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">c<sub>3</sub></font> implies ( <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">c<sub>3</sub></font> ) )
 <b>by </b><i><a class="ref" href="qc_lang2.html#T83" target="_self">Th83</a></i>;<br/>


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