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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E33">th24</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: PL_AXIOM:47</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#R3" title="PL_AXIOM:pred.3">|=</a> <font color="Olive" title="b1">A</font> &amp; <font color="Olive" title="b3">F</font> <a href="pl_axiom.html#R3" title="PL_AXIOM:pred.3">|=</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="pl_axiom.html#R3" title="PL_AXIOM:pred.3">|=</a> <font color="Olive" title="b2">B</font></div></div>
