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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="classes2.html#NM1">Universe</a>;<br/>

<b>assume </b><a NAME="E1:69_1_1"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="classes2.html#NM1">Universe</a> st <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="classes2.html#NM1">Universe</a> st <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:69_1_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></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">E47</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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