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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/>





<b>assume </b><a NAME="E1:96"/><i><font color="Green">E60</font></i>: 
( ( <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R1" target="_self">is_immediate_constituent_of</a> <font color="Maroon">c<sub>2</sub></font> or <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>2</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">c<sub>2</sub></font> ) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:96"/><b>then </b>
( <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>2</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T73" target="_self">Th73</a></i>;<br/>
<a NAME="E3:96"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">c<sub>2</sub></font> &amp; <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> )
 
<b>by </b><i><a class="txt" href="qc_lang2.html#E1:96"><i><font color="Green">E60</font></i></a>, <a class="ref" href="qc_lang2.html#D22" target="_self">Def22</a>, <a class="ref" href="qc_lang2.html#T103" target="_self">Th103</a></i>;<br/>
<a NAME="E4:96"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T77" target="_self">Th77</a></i>;<br/>
<b>hence </b><a NAME="E5:96"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang2.html#K15" target="_self">Subformulae</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="qc_lang2.html#D23" target="_self">Def23</a></i>;<br/>


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