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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>





<b>thus </b><a NAME="E1:46"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">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>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f</font> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">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>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c3">f</font></span>)</span> )
 <b>by </b><i><a class="ref" href="funct_4.html#D2" target="_self" title="FUNCT_4:def.2">Def2</a></i>;<br/>

<b>assume </b><a NAME="E2:46"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">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>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="funct_4.html#K2" title="FUNCT_4:func.2">~</a> <font color="Maroon" title="c3">f</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">x1</font>, <font color="Maroon" title="c5">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:46"/><i><font color="Green" title="E27">A1</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c4">x1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E5:46"/><i><font color="Green" title="E28">A2</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c5">y1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="ref" href="funct_4.html#D2" target="_self" title="FUNCT_4:def.2">Def2</a></i>;<br/>
<a NAME="E6:46"/>
( <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Maroon" title="c5">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )
 
<b>by </b><i><a class="txt" href="funct_4.html#E4:46"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E7:46"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">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>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="txt" href="funct_4.html#E5:46"><i><font color="Green" title="E28">A2</font></i></a></i>;<br/>


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