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<span class="kw">let </span><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="pl_axiom.html#K1" title="PL_AXIOM:func.1">PL-WFF</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G</font> &amp;  not <font color="Maroon" title="c1">F</font> is  <a href="pl_axiom.html#V8" title="PL_AXIOM:attr.8">consistent</a>  implies  not <font color="Maroon" title="c2">G</font> is  <a href="pl_axiom.html#V8" title="PL_AXIOM:attr.8">consistent</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:100"/><span class="lab"><font color="Green" title="E58">A2</font></span>: 
( <font color="Maroon" title="c1">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G</font> &amp;  not <font color="Maroon" title="c1">F</font> is  <a href="pl_axiom.html#V8" title="PL_AXIOM:attr.8">consistent</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c2">G</font> is  <a href="pl_axiom.html#V8" title="PL_AXIOM:attr.8">consistent</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="pl_axiom.html#K1" title="PL_AXIOM:func.1">PL-WFF</a> <span class="kw"> such that </span><br/><a NAME="E3:100"/><span class="lab"><font color="Green" title="E59">A1</font></span>: 
( <font color="Maroon" title="c1">F</font> <a href="pl_axiom.html#R6" title="PL_AXIOM:pred.6">|-</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c1">F</font> <a href="pl_axiom.html#R6" title="PL_AXIOM:pred.6">|-</a>  <a href="pl_axiom.html#K6" title="PL_AXIOM:func.6">'not'</a> <font color="Maroon" title="c3">p</font> )
 ;<br/>
<a NAME="E4:100"/>
( <font color="Maroon" title="c2">G</font> <a href="pl_axiom.html#R6" title="PL_AXIOM:pred.6">|-</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c2">G</font> <a href="pl_axiom.html#R6" title="PL_AXIOM:pred.6">|-</a>  <a href="pl_axiom.html#K6" title="PL_AXIOM:func.6">'not'</a> <font color="Maroon" title="c3">p</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pl_axiom.html#T55" target="_self" onmouseover="rs('pl_axiom/T55')" onmouseout="rh()">monmp</a>, <a class="txt" href="#E3:100"><span class="lab"><font color="Green" title="E59">A1</font></span></a>, <a class="txt" href="#E1:100"><span class="lab"><font color="Green" title="E58">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:100"/>
 not <font color="Maroon" title="c2">G</font> is  <a href="pl_axiom.html#V8" title="PL_AXIOM:attr.8">consistent</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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