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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">U</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>;<br/>



<b>assume </b><a NAME="E1:56"/><i><font color="Green" title="E43">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">U</font>
 ;<br/>

<b>hence </b><a NAME="E2:56"/>
 <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">U</font>
 <b>by </b><i><a class="ref" href="classes1.html#D2" title="CLASSES1:def.2">CLASSES1:def 2</a></i>;<br/>

<a NAME="E3:56"/>
( <font color="Maroon" title="c2">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c2">U</font></span>)</span> &amp;  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c2">U</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c2">U</font> <a href="ordinal1.html#NR2" title="ORDINAL1:NR.2">is_limit_ordinal</a>  )
 
<b>by </b><i><a class="ref" href="classes2.html#T54" target="_self" title="CLASSES2:th.54">Th54</a>, <a class="ref" href="classes2.html#T55" target="_self" title="CLASSES2:th.55">Th55</a></i>;<br/>
<b>hence </b><a NAME="E4:56"/><i><font color="Green" title="E44">A2</font></i>: 
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">U</font>
 <b>by </b><i><a class="txt" href="classes2.html#E1:56"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="classes1.html#T41" title="CLASSES1:th.41">CLASSES1:41</a></i>;<br/>

<a NAME="E5:56"/>
 <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#T3" title="SETFAM_1:th.3">SETFAM_1:3</a></i>;<br/>
<b>hence </b><a NAME="E6:56"/>
 <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">U</font>
 <b>by </b><i><a class="txt" href="classes2.html#E4:56"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="classes1.html#D1" title="CLASSES1:def.1">CLASSES1:def 1</a></i>;<br/>


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