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<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">Y</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">Z</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:11"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">X</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">Y</font>
 <b>and </b><br/><a NAME="E2:11"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">Y</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">Z</font>
 ;<br/>

<a NAME="E3:11"/>
for <font color="Olive">p</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>   st <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> holds <br/><font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <font color="Olive">p</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<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>assume </b><a NAME="E1:11_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 ;<br/>

<a NAME="E2:11_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:11_1"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1">Cn</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D9">CQC_THE1:def 9</a></i>;<br/>
<a NAME="E4:11_1"/>
<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="cqc_the1.html#K1">Cn</a> <font color="Maroon">X</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:11_1"/><b>then </b>
 <a href="cqc_the1.html#K1">Cn</a> <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="cqc_the1.html#K1">Cn</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:11_1"/>
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="cqc_the1.html#D9">CQC_THE1:def 9</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:11"/>
<font color="Maroon">X</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">Z</font>
 <b>by </b><i/>;<br/>


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