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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E45">th42</font></span>: <a NAME="T53"><span class="comment"><font color="firebrick">:: PL_AXIOM:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</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 ( <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pl_axiom.html#K12" title="PL_AXIOM:func.12">PL_axioms</a>  or <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">F</font> ) holds <br/><font color="Olive" title="b2">F</font> <a href="pl_axiom.html#R6" title="PL_AXIOM:pred.6">|-</a> <font color="Olive" title="b1">p</font></div></div>
