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<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">I</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">EqR</font> be   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">c1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font>, <font color="Maroon">c2</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:6"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">c1</font>
 <b>and </b><br/><a NAME="E2:6"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">c2</font>
 ;<br/>

<b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:6"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E5:6"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">x1</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">x2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:6"/>
<font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E8:6"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c2</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">x2</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/>
<a NAME="E9:6"/><i><font color="Green">E45</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">x1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">EqR</font>
 
<b>by </b><i>, , <a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/>
<a NAME="E10:6"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">x2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">EqR</font>
 
<b>by </b><i>, , <a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/>
<b>then </b> <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">x2</font> = 
 <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="eqrel_1.html#T44">EQREL_1:44</a></i>
<br/>.= 
<font color="Maroon">c1</font>
<b>by </b><i>, , , <a class="ref" href="eqrel_1.html#T44">EQREL_1:44</a></i>
;<br/>
<b>hence </b><a NAME="E12:6"/>
<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c2</font>
 <b>by </b><i/>;<br/>


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