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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">U</font> be   <a href="classes2.html#NM1">Universe</a>;<br/>





<b>assume </b><a NAME="E1:57"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U</font> )
 ;<br/>

<a NAME="E2:57"/><b>then </b>
( <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">U</font> &amp;  <a href="tarski.html#K3">union</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font> &amp;  <a href="setfam_1.html#K1">meet</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font> )
 
<b>by </b><i>, <a class="ref" href="setfam_1.html#T12">SETFAM_1:12</a>, <a class="ref" href="zfmisc_1.html#T93">ZFMISC_1:93</a></i>;<br/>
<b>hence </b><a NAME="E3:57"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U</font> &amp; <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U</font> )
 <b>by </b><i/>;<br/>

<a NAME="E4:57"/>
( <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> &amp; <font color="Maroon">X</font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T101">XBOOLE_1:101</a></i>;<br/>
<b>hence </b><a NAME="E5:57"/>
( <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U</font> &amp; <font color="Maroon">X</font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U</font> )
 <b>by </b><i><a class="ref" href="classes2.html#T12" target="_self">Th12</a>, <a class="ref" href="classes2.html#T14" target="_self">Th14</a>, <a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>


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