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<div class="add">

<b>let </b><font color="Maroon">X</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">Y</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="E1:141"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 ;<br/>

<b>thus </b><a NAME="E2:141"/>
 <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">Y</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="141_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</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="E1:141_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">t</font> = <font color="Maroon">a</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="E3:141_1"/>
for <font color="Olive">T</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">T</font> is <a href="intpro_1.html#V10" target="_self">S4_theory</a> &amp; <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">T</font> holds <br/><font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Olive">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="141_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">T</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="E1:141_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">T</font> is <a href="intpro_1.html#V10" target="_self">S4_theory</a>
 <b>and </b><br/><a NAME="E2:141_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">T</font>
 ;<br/>

<a NAME="E3:141_1_1"/>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T38" target="_self">Th38</a>, <a class="ref" href="intpro_1.html#T43" target="_self">Th43</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:141_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T39" target="_self">Th39</a>, <a class="ref" href="intpro_1.html#T42" target="_self">Th42</a>, <a class="ref" href="intpro_1.html#T26" target="_self">Th26</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:141_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T26" target="_self">Th26</a></i>;<br/>


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


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