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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">EqR</font> be   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:39"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>and </b><br/><a NAME="E2:39"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c2">EqR</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c2">EqR</font>;<br/>
<a NAME="E4:39"/>
<font color="Maroon" title="c3">z</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E2:39"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E5:39"/><b>then </b>
 ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c2">EqR</font>,<font color="Olive" title="b1">x</font> )
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E2:39"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="eqrel_1.html#D5" target="_self" title="EQREL_1:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
contradiction
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:39"><i><font color="Green" title="E21">A1</font></i></a></i>;<br/>


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