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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: HILBERT1:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="hilbert1.html#K1" title="HILBERT1:func.1">HP-WFF</a>  holds <br/> ( <font color="Olive" title="b1">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Olive" title="b2">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="hilbert1.html#K6" title="HILBERT1:func.6">HP_TAUT</a>  iff ( <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="hilbert1.html#K6" title="HILBERT1:func.6">HP_TAUT</a>  &amp; <font color="Olive" title="b2">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="hilbert1.html#K6" title="HILBERT1:func.6">HP_TAUT</a>  ) )</div></div>
