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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E34">withplax</font></span>   defines <a href="pl_axiom.html#V4" title="PL_AXIOM:attr.4">with_PL_axioms</a> <a onclick="hs(this)" href="javascript:()">PL_AXIOM:def 19 : <br/></a><span> for <font color="Olive" title="b1">D</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b1">D</font> is  <a href="pl_axiom.html#V4" title="PL_AXIOM:attr.4">with_PL_axioms</a>  iff  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font>, <font color="Olive" title="b4">r</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>  holds <br/> ( <font color="Olive" title="b2">p</font> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">q</font> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <font color="Olive" title="b2">p</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">D</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">p</font> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">q</font> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <font color="Olive" title="b4">r</font></span>)</span></span>)</span> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">p</font> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <font color="Olive" title="b3">q</font></span>)</span> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">p</font> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <font color="Olive" title="b4">r</font></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">D</font> &amp; <span class="p1">(<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="b3">q</font></span>)</span> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <span class="p2">(<span class="default"><a href="pl_axiom.html#K6" title="PL_AXIOM:func.6">'not'</a> <font color="Olive" title="b2">p</font></span>)</span></span>)</span> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pl_axiom.html#K6" title="PL_AXIOM:func.6">'not'</a> <font color="Olive" title="b3">q</font></span>)</span> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <font color="Olive" title="b2">p</font></span>)</span> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <font color="Olive" title="b3">q</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">D</font> ) );<br/></span></div>
