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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font> implies <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font> )</span><br/>



<b>assume </b><a NAME="E1:73"/><i><font color="Green" title="E53">A1</font></i>: 
(  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">B</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:73"/><b>then </b>
( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> or <font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#T24" title="ORDINAL1:th.24">ORDINAL1:24</a></i>;<br/>
<a NAME="E3:73"/><b>then </b>
(  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font> or  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <font color="Maroon" title="c1">A</font> )
 
<b>by </b><i><a class="ref" href="classes2.html#T80" target="_self" title="CLASSES2:th.80">Th80</a></i>;<br/>
<b>hence </b><a NAME="E4:73"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:73"><i><font color="Green" title="E53">A1</font></i></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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