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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: PL_AXIOM:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</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  <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <font color="Olive" title="b2">q</font></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"><a href="pl_axiom.html#K6" title="PL_AXIOM:func.6">'not'</a> <font color="Olive" title="b2">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="b1">p</font></span>)</span></span>)</span> is  <a href="pl_axiom.html#V3" title="PL_AXIOM:attr.3">tautology</a> </div></div>
