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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="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/><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="E1:113"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="intpro_1.html#K1" target="_self">MC-wff</a>  ;<br/>
<a NAME="E3:113"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="intpro_1.html#K1" target="_self">MC-wff</a>  st <font color="Olive">b<sub>1</sub></font> is <a href="intpro_1.html#V9" target="_self">CPC_theory</a> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:113_1"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="intpro_1.html#V9" target="_self">CPC_theory</a>
 <b>and </b><br/><a NAME="E2:113_1"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E3:113_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="intpro_1.html#V8" target="_self">IPC_theory</a>
 
<b>by </b><i><a class="txt" href="intpro_1.html#E1:113_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="intpro_1.html#T67" target="_self">Th67</a></i>;<br/>
<b>hence </b><a NAME="E4:113_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:113"><i><font color="Green">E83</font></i></a>, <a class="txt" href="intpro_1.html#E2:113_1"><i><font color="Green">E85</font></i></a>, <a class="ref" href="intpro_1.html#D15" target="_self">Def15</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:113"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="intpro_1.html#D20" target="_self">Def20</a></i>;<br/>


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