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<div>:: <span class="kw">deftheorem </span>   defines <a href="ltlaxio3.html#V1" title="LTLAXIO3:attr.1">without_implication</a> <a onclick="hs(this)" href="javascript:()">LTLAXIO3:def 1 : <br/></a><span> for <font color="Olive" title="b1">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> holds <br/> ( <font color="Olive" title="b1">X</font> is  <a href="ltlaxio3.html#V1" title="LTLAXIO3:attr.1">without_implication</a>  iff  for <font color="Olive" title="b2">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_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">X</font> holds <br/> not <font color="Olive" title="b2">p</font> is  <a href="hilbert2.html#V2" title="HILBERT2:attr.2">conditional</a>  );<br/></span></div>
