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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">B</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="rfunct_3.html#K4">PFuncs</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span>;<br/>



<a NAME="E1:2"/>
<font color="Maroon">B</font> is <a href="fraenkel.html#V1">functional</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="fraenkel.html#D1">FRAENKEL:def 1</a><br/>

<b>assume </b><a NAME="E1:2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/>

<b>hence </b><a NAME="E2:2_1"/>
<font color="Maroon">x</font> is   <a href="funct_1.html#NM1">Function</a>
 <b>by </b><i><a class="ref" href="partfun1.html#T120">PARTFUN1:120</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:2"/>
<font color="Maroon">B</font> is  non <a href="xboole_0.html#V1">empty</a> <a href="fraenkel.html#V1">functional</a>  <a href="hidden.html#M1">set</a> 
 ;<br/>


</div>
