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<b>let </b><font color="Maroon" title="c1">q</font>, <font color="Maroon" title="c2">r</font>, <font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">s</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c1">q</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K6" title="HILBERT1:func.6">HP_TAUT</a> </span><br/>







<a NAME="E1:42"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c1">q</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K6" title="HILBERT1:func.6">HP_TAUT</a> 
 
<b>by </b><i><a class="ref" href="hilbert1.html#T21" target="_self" title="HILBERT1:th.21">Th21</a></i>;<br/>
<b>hence </b><a NAME="E2:42"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c2">r</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c1">q</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K6" title="HILBERT1:func.6">HP_TAUT</a> 
 <b>by </b><i><a class="ref" href="hilbert1.html#T22" target="_self" title="HILBERT1:th.22">Th22</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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