<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="qc_lang1.html#M1">QC-variable_list</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:63"/>
<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> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:63"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a>  st <font color="Olive">b<sub>1</sub></font> <a href="qc_lang2.html#R1" target="_self">is_immediate_constituent_of</a> <font color="Maroon">c<sub>3</sub></font> <a href="qc_lang1.html#K9">!</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T75" target="_self">Th75</a></i>;<br/>
<b>hence </b><a NAME="E3:63"/>
contradiction
 <b>by </b><i><a class="ref" href="qc_lang2.html#T59" target="_self">Th59</a></i>;<br/>


</div>
