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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E33">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: HILBERT2:32</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   <a href="hilbert2.html#K3" title="HILBERT2:func.3">Subformulae</a> <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">(<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="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<span class="p1">(<span class="default"><a href="hilbert2.html#K3" title="HILBERT2:func.3">Subformulae</a> <font color="Olive" title="b1">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="hilbert2.html#K3" title="HILBERT2:func.3">Subformulae</a> <font color="Olive" title="b2">q</font></span>)</span>)</div></div>
