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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="E1:142"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <span class="p1">(<span class="default"><a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<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="E3:142"/>
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#V10" target="_self">S4_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="142_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="E1:142_1"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="intpro_1.html#V10" target="_self">S4_theory</a>
 <b>and </b><br/><a NAME="E2:142_1"/><i><font color="Green">E108</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="E3:142_1"/>
 <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="intpro_1.html#E1:142_1"><i><font color="Green">E107</font></i></a>, <a class="txt" href="intpro_1.html#E2:142_1"><i><font color="Green">E108</font></i></a>, <a class="ref" href="intpro_1.html#T88" target="_self">Th88</a></i>;<br/>
<b>hence </b><a NAME="E4:142_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#E1:142"><i><font color="Green">E106</font></i></a>, <a class="txt" href="intpro_1.html#E1:142_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="intpro_1.html#D23" target="_self">Def23</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:142"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="intpro_1.html#D23" target="_self">Def23</a></i>;<br/>


</div>
