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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:38"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E2:38"/><i><font color="Green">E23</font></i>: 
 <a href="eqrel_1.html#K8" target="_self">Class</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="eqrel_1.html#K8" target="_self">Class</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E4:38"/>
<font color="Maroon">c<sub>3</sub></font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E2:38"><i><font color="Green">E23</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E5:38"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E2:38"><i><font color="Green">E23</font></i></a>, <a class="ref" href="eqrel_1.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E6:38"/>
contradiction
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:38"><i><font color="Green">E22</font></i></a></i>;<br/>


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