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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">r</font>, <font color="Maroon" title="c4">s</font> be   <a href="xboolean.html#V1" title="XBOOLEAN:attr.1">boolean</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="xboolean.html#K7" title="XBOOLEAN:func.7">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboolean.html#K2" title="XBOOLEAN:func.2">TRUE</a>  &amp; <font color="Maroon" title="c3">r</font> <a href="xboolean.html#K7" title="XBOOLEAN:func.7">&lt;=&gt;</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboolean.html#K2" title="XBOOLEAN:func.2">TRUE</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="xboolean.html#K7" title="XBOOLEAN:func.7">&lt;=&gt;</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="xboolean.html#K7" title="XBOOLEAN:func.7">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="xboolean.html#K7" title="XBOOLEAN:func.7">&lt;=&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboolean.html#K2" title="XBOOLEAN:func.2">TRUE</a>  )</span><br/>







<a NAME="E1:132"/>
( <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboolean.html#K1" title="XBOOLEAN:func.1">FALSE</a>  or <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboolean.html#K2" title="XBOOLEAN:func.2">TRUE</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#D3" target="_self" title="XBOOLEAN:def.3">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:132"/>
( <font color="Maroon" title="c1">p</font> <a href="xboolean.html#K7" title="XBOOLEAN:func.7">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboolean.html#K2" title="XBOOLEAN:func.2">TRUE</a>  &amp; <font color="Maroon" title="c3">r</font> <a href="xboolean.html#K7" title="XBOOLEAN:func.7">&lt;=&gt;</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboolean.html#K2" title="XBOOLEAN:func.2">TRUE</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="xboolean.html#K7" title="XBOOLEAN:func.7">&lt;=&gt;</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="xboolean.html#K7" title="XBOOLEAN:func.7">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="xboolean.html#K7" title="XBOOLEAN:func.7">&lt;=&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboolean.html#K2" title="XBOOLEAN:func.2">TRUE</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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