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

<b>set </b><font color="Maroon" title="c2">B</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<a NAME="E1:14_1_1"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T80" title="ZFMISC_1:th.80">ZFMISC_1:80</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">B</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c3">B</font>
;<br/>

<a NAME="E3:14_1_1"/>
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:14_1_1"/>
<font color="Maroon" title="c3">B</font> is <a href="armstrng.html#V1" title="ARMSTRNG:attr.1">(B1)</a>
 <b>by </b><i><a class="ref" href="armstrng.html#D4" target="_self" title="ARMSTRNG:def.4">Def4</a></i>;<br/>

<b>thus </b><a NAME="E5:14_1_1"/>
<font color="Maroon" title="c3">B</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">(B2)</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="finsub_1.html#D2" title="FINSUB_1:def.2">FINSUB_1:def 2</a><br/>

<b>assume </b><a NAME="E1:14_1_1_1"/>
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> )
 ;<br/>

<a NAME="E2:14_1_1_1"/><b>then </b>
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:14_1_1_1"/>
<font color="Maroon" title="c4">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>


</div>
