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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>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/>





<b>assume </b><a NAME="E1:134"/><i><font color="Green">E98</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> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</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> )
 ;<br/>

<a NAME="E2:134"/>
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="134_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><a NAME="E1:134_1"/><i><font color="Green">E99</font></i>: 
( <font color="Maroon">c<sub>4</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="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E2:134_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <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#E1:134"><i><font color="Green">E98</font></i></a>, <a class="ref" href="intpro_1.html#D23" target="_self">Def23</a></i>;<br/>
<b>hence </b><a NAME="E3:134_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#E1:134_1"><i><font color="Green">E99</font></i></a>, <a class="ref" href="intpro_1.html#D22" target="_self">Def22</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:134"/>
<font color="Maroon">c<sub>3</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>
