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<b>let </b><font color="Maroon" title="c2">T1</font>, <font color="Maroon" title="c3">T2</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>;<br/>

<b>assume </b><a NAME="E1:69_1_1"/><i><font color="Green" title="E48">A1</font></i>: 
( <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">T1</font> &amp; ( for <font color="Olive" title="b1">Y</font> being  <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>  st <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Y</font> holds <br/><font color="Maroon" title="c2">T1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Y</font> ) &amp; <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">T2</font> &amp; ( for <font color="Olive" title="b1">Y</font> being  <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>  st <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Y</font> holds <br/><font color="Maroon" title="c3">T2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Y</font> ) &amp; not <font color="Maroon" title="c2">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">T2</font> )
 ;<br/>

<a NAME="E2:69_1_1"/><b>then </b>
( <font color="Maroon" title="c2">T1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">T2</font> &amp; <font color="Maroon" title="c3">T2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">T1</font> )
 
;<br/>
<b>hence </b><a NAME="E3:69_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="classes2.html#E1:69_1_1"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


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