<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">Y</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">P</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>, <font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:7_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="partit1.html#K4">ERl</a> <font color="Maroon">P</font>
 ;<br/><a NAME="E2:7_1"/><b>then </b>
 ex <font color="Olive">A</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">Y</font> st <br/>( <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">A</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">A</font> )
 <b>by </b><i><a class="ref" href="partit1.html#D6">PARTIT1:def 6</a></i>;<br/><b>hence </b><a NAME="E3:7_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">y</font>,<font color="Maroon">P</font>
 <b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/></div>
<b>end;</b></div>

<a NAME="E2:7"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">y</font>,<font color="Maroon">P</font> &amp;  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">y</font>,<font color="Maroon">P</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:7"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">y</font>,<font color="Maroon">P</font> implies <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="partit1.html#K4">ERl</a> <font color="Maroon">P</font> )
 <b>by </b><i><a class="ref" href="partit1.html#D6">PARTIT1:def 6</a></i>;<br/>


</div>
