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

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

<a NAME="E1:50"/>
 <a href="setfam_1.html#K2">UNION</a> <a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">F</font> <a href="tarski.html#R1">c=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_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="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:50_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K2">UNION</a> <a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">F</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:50_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">x2</font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D4">SETFAM_1:def 4</a></i>;<br/>
<b>thus </b><a NAME="E4:50_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:50"/>
 <a href="setfam_1.html#K2">UNION</a> <a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>


</div>
