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<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>thus </b><a NAME="E1:33"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#NR1" target="_self">is_a_theory</a>  implies  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:33_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#NR1" target="_self">is_a_theory</a> 
 ;<br/>

<a NAME="E2:33_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <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="ref" href="cqc_the1.html#T38" target="_self">Th38</a></i>;<br/>
<a NAME="E3:33_1"/>
 <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:33_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>hence </b><a NAME="E2:33_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the1.html#E1:33_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="cqc_the1.html#D2" target="_self">Def2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:33_1"/>
 <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the1.html#E2:33_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:33"/>
(  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#NR1" target="_self">is_a_theory</a>  )
 <b>by </b><i><a class="ref" href="cqc_the1.html#T36" target="_self">Th36</a></i>;<br/>


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