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<div class="add">

<b>let </b><font color="Maroon">X</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">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">q</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/>







<b>assume </b><a NAME="E1:16"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">X</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">p</font> )
 ;<br/>

<a NAME="E2:16"/>
for <font color="Olive">T</font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a>   st <font color="Olive">T</font> <a href="cqc_the1.html#NR1" target="_self">is_a_theory</a>  &amp; <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Olive">T</font> holds <br/><font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Olive">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">T</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:16_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">T</font> <a href="cqc_the1.html#NR1" target="_self">is_a_theory</a>  &amp; <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">T</font> )
 ;<br/>

<a NAME="E2:16_1"/><b>then </b>
<font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:16_1"/>
<font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:16"/>
<font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>


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