<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E18">Def5</font></span>   defines <a href="pl_axiom.html#V2" title="PL_AXIOM:attr.2">PL-closed</a> <a onclick="hs(this)" href="javascript:()">PL_AXIOM:def 2 : <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#V2" title="PL_AXIOM:attr.2">PL-closed</a>  iff ( <font color="Olive" title="b1">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  &amp; <font color="Olive" title="b1">D</font> is  <a href="intpro_1.html#V1" title="INTPRO_1:attr.1">with_FALSUM</a>  &amp; <font color="Olive" title="b1">D</font> is  <a href="hilbert1.html#V2" title="HILBERT1:attr.2">with_implication</a>  &amp; <font color="Olive" title="b1">D</font> is  <a href="pl_axiom.html#V1" title="PL_AXIOM:attr.1">with_propositional_variables</a>  ) );<br/></span></div>
