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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: HILBERT3:31</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> <br/>  for <font color="Olive" title="b3">V</font> being   <a href="hilbert3.html#NM1" title="HILBERT3:NM.1">SetValuation</a> holds   <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> (<font color="Olive" title="b3">V</font>,<span class="p1">(<span class="default"><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></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> (<font color="Olive" title="b3">V</font>,<font color="Olive" title="b1">p</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> (<font color="Olive" title="b3">V</font>,<font color="Olive" title="b2">q</font>)</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert3.html#D2" target="_self" onmouseover="rs('hilbert3/D2')" onmouseout="rh()">Def2</a></span>;<br/></div></div>
