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<div><span class="kw">theorem </span><a NAME="T59"><span class="comment"><font color="firebrick">:: PL_AXIOM:59</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</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="b3">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 <font color="Olive" title="b3">F</font> <a href="pl_axiom.html#R6" title="PL_AXIOM:pred.6">|-</a> <font color="Olive" title="b1">A</font> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <font color="Olive" title="b2">B</font> holds <br/><font color="Olive" title="b3">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"><font color="Olive" title="b1">A</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="pl_axiom.html#R6" title="PL_AXIOM:pred.6">|-</a> <font color="Olive" title="b2">B</font></div></div>
