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

<b>assume </b><b>that </b><br/><a NAME="E1:52"/><i><font color="Green">E37</font></i>: 
 <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">F</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E2:52"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<b>consider </b><font color="Maroon">X</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:52"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="txt" href="topgen_4.html#E3"><i><font color="Green">Lemma30</font></i></a>, <a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">Y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:52"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="txt" href="topgen_4.html#E3"><i><font color="Green">Lemma30</font></i></a>, <a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E7:52"/>
<font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">F</font>,<font color="Maroon">G</font>
 
<b>by </b><i>, , <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E8:52"/>
contradiction
 <b>by </b><i/>;<br/>


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