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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:17"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E2:17"/>
 ex <font color="Olive">f</font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <font color="Olive">f</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">f</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>take </b>
 <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font>
;<br/>

<b>thus </b><a NAME="E1:17_1"/>
(  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#T52">FUNCT_1:52</a>, <a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:17"/>
 <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/>


</div>
