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<span class="kw">let </span><font color="Maroon" title="c1">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is  <a href="intpro_1.html#V8" title="INTPRO_1:attr.8">IPC_theory</a>  iff  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> implies <font color="Maroon" title="c1">T</font> is  <a href="intpro_1.html#V8" title="INTPRO_1:attr.8">IPC_theory</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:40_1"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
<font color="Maroon" title="c1">T</font> is  <a href="intpro_1.html#V8" title="INTPRO_1:attr.8">IPC_theory</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font></span><br/><a NAME="E2:40_1"/><span class="lab"><font color="Green" title="E29">A2</font></span>: 
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">T</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">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">T</font> or <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:40_1_1"/>
<font color="Maroon" title="c2">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">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font></span><br/>

<span class="kw">hence </span><a NAME="E2:40_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="intpro_1.html#D15" target="_self" title="INTPRO_1:def.15">Def15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:40_1"/>
<font color="Maroon" title="c1">T</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="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T12" target="_self" title="INTPRO_1:th.12">Th12</a></span>;<br/><span class="kw">hence </span><a NAME="E4:40_1"/>
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:40_1"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E2:40"/>
(  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> implies <font color="Maroon" title="c1">T</font> is  <a href="intpro_1.html#V8" title="INTPRO_1:attr.8">IPC_theory</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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