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<b>let </b><font color="Maroon">A</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E1:75"/><i><font color="Green">E27</font></i>: 
(  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">B</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B</font> )
 ;<br/>

<a NAME="E2:75"/><b>then </b>
( <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> or <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#T24">ORDINAL1:24</a></i>;<br/>
<a NAME="E3:75"/><b>then </b>
(  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">B</font> or  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="classes2.html#K16" target="_self">UNIVERSE</a> <font color="Maroon">A</font> )
 
<b>by </b><i><a class="ref" href="classes2.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E4:75"/>
contradiction
 <b>by </b><i/>;<br/>


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