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

<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><a NAME="E1:3"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> holds <br/><font color="Olive">x</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">y</font>
 ;<br/>

<a NAME="E2:3"/>
for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> holds <br/> <a href="tarski.html#K3">union</a> <font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1"><b>proof </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="E1:3_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/>

<a NAME="E2:3_1"/><b>then </b>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">x</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:3_1"/>
 <a href="tarski.html#K3">union</a> <font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T98">ZFMISC_1:98</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:3"/>
 <a href="tarski.html#K3">union</a> <font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T98">ZFMISC_1:98</a></i>;<br/>


</div>
