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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E54">th34</font></span>: <a NAME="T63"><span class="comment"><font color="firebrick">:: PL_AXIOM:63</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</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> <br/>  for <font color="Olive" title="b2">F</font> being   <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>  st  not <font color="Olive" title="b2">F</font> <a href="pl_axiom.html#R6" title="PL_AXIOM:pred.6">|-</a> <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b2">F</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="pl_axiom.html#K6" title="PL_AXIOM:func.6">'not'</a> <font color="Olive" title="b1">A</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is  <a href="pl_axiom.html#V8" title="PL_AXIOM:attr.8">consistent</a> </div></div>
