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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> implies  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c2">Y</font> )</span><br/>



<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c2">Y</font></span><br/>

<b>thus </b><a NAME="E2:35"/>
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c2">Y</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c2">Y</font> )</span><br/>

<b>assume </b><a NAME="E1:35_1"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c2">Y</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c4">t</font> = <font color="Maroon" title="c3">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a>  ;<br/>
<a NAME="E3:35_1"/>
for <font color="Olive" title="b1">T</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a>   st <font color="Olive" title="b1">T</font> is <a href="intpro_1.html#V8" title="INTPRO_1:attr.8">IPC_theory</a> &amp; <font color="Maroon" title="c2">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">T</font> holds <br/><font color="Maroon" title="c4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">T</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">T</font> is <a href="intpro_1.html#V8" title="INTPRO_1:attr.8">IPC_theory</a> &amp; <font color="Maroon" title="c2">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">T</font> implies <font color="Maroon" title="c4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">T</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:35_1_1"/><i><font color="Green" title="E27">A3</font></i>: 
<font color="Maroon" title="c5">T</font> is <a href="intpro_1.html#V8" title="INTPRO_1:attr.8">IPC_theory</a>
 <b>and </b><br/><a NAME="E2:35_1_1"/><i><font color="Green" title="E28">A4</font></i>: 
<font color="Maroon" title="c2">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">T</font></span><br/>

<a NAME="E3:35_1_1"/>
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">T</font>
 
<b>by </b><i><a class="txt" href="intpro_1.html#E1:35"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="intpro_1.html#E2:35_1_1"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:35_1_1"/>
<font color="Maroon" title="c4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">T</font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:35_1"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="intpro_1.html#E1:35_1_1"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="intpro_1.html#D15" target="_self" title="INTPRO_1:def.15">Def15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:35_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#D15" target="_self" title="INTPRO_1:def.15">Def15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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


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