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<div>:: <span class="kw">deftheorem </span>   defines <a href="hilbert1.html#V2" title="HILBERT1:attr.2">with_implication</a> <a onclick="hs(this)" href="javascript:()">PL_AXIOM:def 8 : <br/></a><span> for <font color="Olive" title="b1">D</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> holds <br/> ( <font color="Olive" title="b1">D</font> is  <a href="hilbert1.html#V2" title="HILBERT1:attr.2">with_implication</a>  iff  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">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>   st <font color="Olive" title="b2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">D</font> &amp; <font color="Olive" title="b3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">D</font> holds <br/><font color="Olive" title="b2">p</font> <a href="pl_axiom.html#K3" title="PL_AXIOM:func.3">=&gt;</a> <font color="Olive" title="b3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">D</font> );<br/></span></div>
