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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">EqR1</font>, <font color="Maroon" title="c3">EqR2</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/>





<a NAME="E1:20"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c2">EqR1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K3" title="EQREL_1:func.3">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K4" title="EQREL_1:func.4">/\</a> <font color="Maroon" title="c3">EqR2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T22" title="XBOOLE_1:th.22">XBOOLE_1:22</a></i>;<br/>
<a NAME="E2:20"/>
for <font color="Olive" title="b1">EqR</font> being  <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K3" title="EQREL_1:func.3">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K4" title="EQREL_1:func.4">/\</a> <font color="Maroon" title="c3">EqR2</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">EqR</font> holds <br/><font color="Maroon" title="c2">EqR1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">EqR</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T22" title="XBOOLE_1:th.22">XBOOLE_1:22</a></i>;<br/>
<b>hence </b><a NAME="E3:20"/>
<font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K4" title="EQREL_1:func.4">/\</a> <font color="Maroon" title="c3">EqR2</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">EqR1</font>
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:20"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="eqrel_1.html#D3" target="_self" title="EQREL_1:def.3">Def3</a></i>;<br/>


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