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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="E1:56"/><i><font color="Green">E39</font></i>: 
( <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> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:56_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:56_1"/><b>then </b><i><font color="Green">E40</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="qc_lang2.html#E1:56"><i><font color="Green">E39</font></i></a>, <a class="ref" href="qc_lang2.html#D22" target="_self">Def22</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:56_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:56_1_1"/><b>then </b>
<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="txt" href="qc_lang2.html#E1:56"><i><font color="Green">E39</font></i></a>, <a class="ref" href="qc_lang2.html#D22" target="_self">Def22</a></i>;<br/><a NAME="E3:56_1_1"/><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>3</sub></font>
 <b>by </b><i><a class="txt" href="qc_lang2.html#E2:56_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="qc_lang2.html#T76" target="_self">Th76</a></i>;<br/><b>hence </b><a NAME="E4:56_1_1"/>
<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#D22" target="_self">Def22</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:56_1"/>
<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="txt" href="qc_lang2.html#E1:56"><i><font color="Green">E39</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:56"/>
<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="txt" href="qc_lang2.html#E1:56"><i><font color="Green">E39</font></i></a></i>;<br/>


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