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<b>let </b><font color="Maroon">R</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">B</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E2:1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E3:1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<b>consider </b><font color="Maroon">x0</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/>
<b>consider </b><font color="Maroon">y0</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">B</font>;<br/>
<a NAME="E6:1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">R</font> is    <a href="relset_1.html#M2">Relation</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>
 
<b>by </b><i>, <a class="ref" href="relset_1.html#D1">RELSET_1:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:1_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/><b>reconsider </b><font color="Maroon">y0</font> = <font color="Maroon">y0</font> as    <a href="hidden.html#M1">set</a>  ;<br/><b>take </b><font color="Maroon">y</font> = <font color="Maroon">y0</font>;<br/><b>thus </b><a NAME="E3:1_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> <font color="Maroon">R</font>
 <b>by </b><i>, , , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="relset_1.html#T22">RELSET_1:22</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:1_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/><b>reconsider </b><font color="Maroon">x0</font> = <font color="Maroon">x0</font> as    <a href="hidden.html#M1">set</a>  ;<br/><b>take </b><font color="Maroon">x</font> = <font color="Maroon">x0</font>;<br/><b>thus </b><a NAME="E3:1_2"/>
<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> <font color="Maroon">R</font>
 <b>by </b><i>, , , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>by </b><i>, <a class="ref" href="relset_1.html#T23">RELSET_1:23</a></i>;<br/>


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