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

<b>let </b><font color="Maroon">H</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">F</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">x</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/>





<a NAME="E1:69"/>
<font color="Maroon">H</font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a>  <a href="qc_lang1.html#K14">All</a> <font color="Maroon">x</font>,<font color="Maroon">H</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:69"/>
(  <a href="qc_lang1.html#K14">All</a> <font color="Maroon">x</font>,<font color="Maroon">H</font> <a href="qc_lang2.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">F</font> implies <font color="Maroon">H</font> <a href="qc_lang2.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">F</font> )
 <b>by </b><i/>;<br/>


</div>
