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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</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> ;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:51_1"/>
<font color="Maroon" title="c1">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K6" title="HILBERT1:func.6">HP_TAUT</a> 
 ;<br/><a NAME="E2:51_1"/><b>then </b>
( <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K6" title="HILBERT1:func.6">HP_TAUT</a>  &amp; <font color="Maroon" title="c2">q</font> <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#T31" target="_self" title="HILBERT1:th.31">Th31</a></i>;<br/><b>hence </b><a NAME="E3:51_1"/>
<font color="Maroon" title="c2">q</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c1">p</font> <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#T31" target="_self" title="HILBERT1:th.31">Th31</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:51"/>
<font color="Maroon" title="c2">q</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K6" title="HILBERT1:func.6">HP_TAUT</a> 
 ;<br/>

<a NAME="E3:51"/><b>then </b>
( <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K6" title="HILBERT1:func.6">HP_TAUT</a>  &amp; <font color="Maroon" title="c1">p</font> <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#T31" target="_self" title="HILBERT1:th.31">Th31</a></i>;<br/>
<b>hence </b><a NAME="E4:51"/>
<font color="Maroon" title="c1">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font> <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#T31" target="_self" title="HILBERT1:th.31">Th31</a></i>;<br/>


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