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

<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>, <font color="Maroon" title="c4">E</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><a NAME="E1:36"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c4">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K3" title="EQREL_1:func.3">\/</a> <font color="Maroon" title="c3">EqR2</font>
 ;<br/>

<a NAME="E2:36"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <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> or  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c2">EqR1</font>,<font color="Olive" title="b1">x</font> or  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c3">EqR2</font>,<font color="Olive" title="b1">x</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:36_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:36_1"/><i><font color="Green" title="E21">A2</font></i>: 
not  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c2">EqR1</font>,<font color="Maroon" title="c5">x</font>
 <b>and </b><br/><a NAME="E3:36_1"/><i><font color="Green" title="E22">A3</font></i>: 
not  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c3">EqR2</font>,<font color="Maroon" title="c5">x</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c6">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:36_1"/><i><font color="Green" title="E23">A4</font></i>: 
( ( <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c5">x</font> &amp; not <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c2">EqR1</font>,<font color="Maroon" title="c5">x</font> ) or ( <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c2">EqR1</font>,<font color="Maroon" title="c5">x</font> &amp; not <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c5">x</font> ) )
 <b>by </b><i><a class="txt" href="eqrel_1.html#E2:36_1"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>
<div><i><font color="Green" title="E24">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1"><b>now </b></a><div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:36_1_1"/><i><font color="Green" title="E25">A6</font></i>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c2">EqR1</font>,<font color="Maroon" title="c5">x</font>
 <b>and </b><br/><a NAME="E2:36_1_1"/><i><font color="Green" title="E26">A7</font></i>: 
not <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c5">x</font>
 ;<br/><a NAME="E3:36_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">EqR1</font>
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:36_1_1"><i><font color="Green" title="E25">A6</font></i></a>, <a class="ref" href="eqrel_1.html#T27" target="_self" title="EQREL_1:th.27">Th27</a></i>;<br/><a NAME="E4:36_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font>
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:36"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E5:36_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="eqrel_1.html#E2:36_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="ref" href="eqrel_1.html#T27" target="_self" title="EQREL_1:th.27">Th27</a></i>;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c7">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E8:36_1"/><i><font color="Green" title="E25">A8</font></i>: 
( ( <font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c5">x</font> &amp; not <font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c3">EqR2</font>,<font color="Maroon" title="c5">x</font> ) or ( <font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c3">EqR2</font>,<font color="Maroon" title="c5">x</font> &amp; not <font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c5">x</font> ) )
 <b>by </b><i><a class="txt" href="eqrel_1.html#E3:36_1"><i><font color="Green" title="E22">A3</font></i></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>
<div><i><font color="Green" title="E26">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_2"><b>now </b></a><div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:36_1_2"/><i><font color="Green" title="E27">A10</font></i>: 
<font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c3">EqR2</font>,<font color="Maroon" title="c5">x</font>
 <b>and </b><br/><a NAME="E2:36_1_2"/><i><font color="Green" title="E28">A11</font></i>: 
not <font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c5">x</font>
 ;<br/><a NAME="E3:36_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">z</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">EqR2</font>
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:36_1_2"><i><font color="Green" title="E27">A10</font></i></a>, <a class="ref" href="eqrel_1.html#T27" target="_self" title="EQREL_1:th.27">Th27</a></i>;<br/><a NAME="E4:36_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">z</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font>
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:36"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E5:36_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="eqrel_1.html#E2:36_1_2"><i><font color="Green" title="E28">A11</font></i></a>, <a class="ref" href="eqrel_1.html#T27" target="_self" title="EQREL_1:th.27">Th27</a></i>;<br/></div><b>end;</b></div>
<a NAME="E10:36_1"/><i><font color="Green" title="E27">A12</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font>
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E5:36_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="eqrel_1.html#E6:36_1"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="eqrel_1.html#T27" target="_self" title="EQREL_1:th.27">Th27</a></i>;<br/>
<a NAME="E11:36_1"/>
not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">EqR1</font>
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E5:36_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="eqrel_1.html#E6:36_1"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="eqrel_1.html#T27" target="_self" title="EQREL_1:th.27">Th27</a></i>;<br/>
<a NAME="E12:36_1"/><b>then </b><i><font color="Green" title="E28">A13</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">EqR2</font>
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E1:36"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="eqrel_1.html#E10:36_1"><i><font color="Green" title="E27">A12</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E13:36_1"/><i><font color="Green" title="E29">A14</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">z</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font>
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E8:36_1"><i><font color="Green" title="E25">A8</font></i></a>, <a class="txt" href="eqrel_1.html#E9:36_1"><i><font color="Green" title="E26">A9</font></i></a>, <a class="ref" href="eqrel_1.html#T27" target="_self" title="EQREL_1:th.27">Th27</a></i>;<br/>
<a NAME="E14:36_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c7">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#T12" target="_self" title="EQREL_1:th.12">Th12</a></i>;<br/>
<a NAME="E15:36_1"/><b>then </b><i><font color="Green" title="E30">A15</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font>
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E10:36_1"><i><font color="Green" title="E27">A12</font></i></a>, <a class="ref" href="eqrel_1.html#T13" target="_self" title="EQREL_1:th.13">Th13</a></i>;<br/>
<a NAME="E16:36_1"/>
not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">z</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">EqR2</font>
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E8:36_1"><i><font color="Green" title="E25">A8</font></i></a>, <a class="txt" href="eqrel_1.html#E9:36_1"><i><font color="Green" title="E26">A9</font></i></a>, <a class="ref" href="eqrel_1.html#T27" target="_self" title="EQREL_1:th.27">Th27</a></i>;<br/>
<a NAME="E17:36_1"/><b>then </b><i><font color="Green" title="E31">A16</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">z</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">EqR1</font>
 
<b>by </b><i><a class="txt" href="eqrel_1.html#E1:36"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="eqrel_1.html#E13:36_1"><i><font color="Green" title="E29">A14</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<div><i><font color="Green" title="E32">A17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:36_1_3"/><i><font color="Green" title="E33">A18</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">EqR2</font>
 ;<br/><a NAME="E2:36_1_3"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">EqR2</font>
 <b>by </b><i><a class="txt" href="eqrel_1.html#E12:36_1"><i><font color="Green" title="E28">A13</font></i></a>, <a class="ref" href="eqrel_1.html#T12" target="_self" title="EQREL_1:th.12">Th12</a></i>;<br/><a NAME="E3:36_1_3"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c7">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">EqR2</font>
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:36_1_3"><i><font color="Green" title="E33">A18</font></i></a>, <a class="ref" href="eqrel_1.html#T13" target="_self" title="EQREL_1:th.13">Th13</a></i>;<br/><a NAME="E4:36_1_3"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">z</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">EqR2</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T12" target="_self" title="EQREL_1:th.12">Th12</a></i>;<br/><b>hence </b><a NAME="E5:36_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="eqrel_1.html#E8:36_1"><i><font color="Green" title="E25">A8</font></i></a>, <a class="txt" href="eqrel_1.html#E9:36_1"><i><font color="Green" title="E26">A9</font></i></a>, <a class="ref" href="eqrel_1.html#T27" target="_self" title="EQREL_1:th.27">Th27</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:36_1_4"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">EqR1</font>
 ;<br/><a NAME="E2:36_1_4"/><b>then </b><i><font color="Green" title="E33">A19</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">z</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">EqR1</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T12" target="_self" title="EQREL_1:th.12">Th12</a></i>;<br/><a NAME="E3:36_1_4"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c7">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">EqR1</font>
 <b>by </b><i><a class="txt" href="eqrel_1.html#E17:36_1"><i><font color="Green" title="E31">A16</font></i></a>, <a class="ref" href="eqrel_1.html#T12" target="_self" title="EQREL_1:th.12">Th12</a></i>;<br/><a NAME="E4:36_1_4"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">EqR1</font>
 <b>by </b><i><a class="txt" href="eqrel_1.html#E2:36_1_4"><i><font color="Green" title="E33">A19</font></i></a>, <a class="ref" href="eqrel_1.html#T13" target="_self" title="EQREL_1:th.13">Th13</a></i>;<br/><a NAME="E5:36_1_4"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">EqR1</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T12" target="_self" title="EQREL_1:th.12">Th12</a></i>;<br/><b>hence </b><a NAME="E6:36_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="eqrel_1.html#E5:36_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="eqrel_1.html#E6:36_1"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="eqrel_1.html#T27" target="_self" title="EQREL_1:th.27">Th27</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E20:36_1"/>
contradiction
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:36"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="eqrel_1.html#E15:36_1"><i><font color="Green" title="E30">A15</font></i></a>, <a class="txt" href="eqrel_1.html#E18:36_1"><i><font color="Green" title="E32">A17</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:36"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <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> or  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c2">EqR1</font>,<font color="Olive" title="b1">x</font> or  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c4">E</font>,<font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <font color="Maroon" title="c3">EqR2</font>,<font color="Olive" title="b1">x</font> )
 ;<br/>


</div>
