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<b>let </b><font color="Maroon" title="c1">T</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ;<br/>

<b>thus </b><a NAME="E1:22"/>
( <font color="Maroon" title="c1">T</font> <a href="cqc_the1.html#NR1" title="CQC_THE1:NR.1">is_a_theory</a>  implies  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c1">T</font> <a href="cqc_the1.html#NR1" title="CQC_THE1:NR.1">is_a_theory</a> 
 ;<br/>

<a NAME="E2:22_1"/><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c1">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="ref" href="cqc_the1.html#T38" target="_self" title="CQC_THE1:th.38">Th38</a></i>;<br/>
<a NAME="E3:22_1"/>
 <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:22_1_1"/>
<font color="Maroon" title="c2">a</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">T</font>
 ;<br/>

<b>hence </b><a NAME="E2:22_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="txt" href="cqc_the1.html#E1:22_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="cqc_the1.html#D2" target="_self" title="CQC_THE1:def.2">Def2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:22_1"/>
 <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="txt" href="cqc_the1.html#E2:22_1"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


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

<b>thus </b><a NAME="E2:22"/>
(  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> implies <font color="Maroon" title="c1">T</font> <a href="cqc_the1.html#NR1" title="CQC_THE1:NR.1">is_a_theory</a>  )
 <b>by </b><i><a class="ref" href="cqc_the1.html#T36" target="_self" title="CQC_THE1:th.36">Th36</a></i>;<br/>


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