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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon" title="c2">s</font> be   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a>;<br/><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>;<br/>







<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E16">A1</font></i>: 
( <font color="Maroon" title="c2">s</font> <a href="cqc_lang.html#K17" title="CQC_LANG:func.17">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a>  &amp; <font color="Maroon" title="c2">s</font> <a href="cqc_lang.html#K17" title="CQC_LANG:func.17">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a>  &amp; not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">s</font> &amp; <font color="Maroon" title="c2">s</font> <a href="cqc_lang.html#K17" title="CQC_LANG:func.17">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">X</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">s1</font> = <font color="Maroon" title="c2">s</font> <a href="cqc_lang.html#K17" title="CQC_LANG:func.17">.</a> <font color="Maroon" title="c3">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c6">q</font> = <font color="Maroon" title="c2">s</font> <a href="cqc_lang.html#K17" title="CQC_LANG:func.17">.</a> <font color="Maroon" title="c4">y</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a>  <b>by </b><i><a class="txt" href="cqc_the1.html#E1:17"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/>
<a NAME="E4:17"/>
for <font color="Olive" title="b1">T</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a>   st <font color="Olive" title="b1">T</font> <a href="cqc_the1.html#NR1" title="CQC_THE1:NR.1">is_a_theory</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">T</font> holds <br/><font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">T</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:17_1"/><i><font color="Green" title="E17">A2</font></i>: 
( <font color="Maroon" title="c7">T</font> <a href="cqc_the1.html#NR1" title="CQC_THE1:NR.1">is_a_theory</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">T</font> )
 ;<br/>

<a NAME="E2:17_1"/><b>then </b>
<font color="Maroon" title="c5">s1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">T</font>
 
<b>by </b><i><a class="txt" href="cqc_the1.html#E1:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="cqc_the1.html#D2" target="_self" title="CQC_THE1:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E3:17_1"/>
<font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">T</font>
 <b>by </b><i><a class="txt" href="cqc_the1.html#E1:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="cqc_the1.html#E1:17_1"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="cqc_the1.html#D1" target="_self" title="CQC_THE1:def.1">Def1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:17"/>
<font color="Maroon" title="c2">s</font> <a href="cqc_lang.html#K17" title="CQC_LANG:func.17">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="cqc_the1.html#D2" target="_self" title="CQC_THE1:def.2">Def2</a></i>;<br/>


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