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<span class="kw">let </span><font color="Maroon" title="c3">P</font> be   <a href="ltlaxio3.html#NV3" title="LTLAXIO3:NV.3">consistent</a>  <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</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  <a href="ltlaxio1.html#NK2" title="LTLAXIO1:NK.2">TFALSUM</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span></span><br/>

<span class="kw">assume </span><a NAME="E1:60"/>
 <a href="ltlaxio1.html#NK2" title="LTLAXIO1:NK.2">TFALSUM</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span>
 ; <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"> contradiction</span><br/>

<a NAME="E2:60"/><span class="kw">then </span>
 <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio1.html#R8" title="LTLAXIO1:pred.8">|-</a>  <a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="ltlaxio3.html#K12" title="LTLAXIO3:func.12">^</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio3.html#T28" target="_self" onmouseover="rs('ltlaxio3/T28')" onmouseout="rh()">Th28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:60"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ltlaxio3.html#D10" target="_self" onmouseover="rs('ltlaxio3/D10')" onmouseout="rh()">Def10</a></span>; <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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