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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:82"/>
 <a href="cqc_the1.html#NR5" target="_self">|-</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:82"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4" target="_self">TAUT</a>  &amp;  <a href="cqc_the1.html#K4" target="_self">TAUT</a>  <a href="tarski.html#R1">c=</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="cqc_the1.html#E118"><i><font color="Green">Lemma54</font></i></a>, <a class="ref" href="cqc_the1.html#T75" target="_self">Th75</a></i>;<br/>
<b>hence </b><a NAME="E3:82"/>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3" target="_self">|-</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the1.html#D9" target="_self">Def9</a></i>;<br/>


</div>
