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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="classes2.html#NM1">Universe</a>;<br/>



<b>assume </b><a NAME="E1:56"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>hence </b><a NAME="E2:56"/>
 <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="classes1.html#D2">CLASSES1:def 2</a></i>;<br/>

<a NAME="E3:56"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="classes1.html#K4">Rank</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K3">On</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="ordinal1.html#K3">On</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="ordinal1.html#K3">On</a> <font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a>  )
 
<b>by </b><i><a class="ref" href="classes2.html#T54" target="_self">Th54</a>, <a class="ref" href="classes2.html#T55" target="_self">Th55</a></i>;<br/>
<b>hence </b><a NAME="E4:56"/><i><font color="Green">E44</font></i>: 
 <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="classes2.html#E1:56"><i><font color="Green">E43</font></i></a>, <a class="ref" href="classes1.html#T41">CLASSES1:41</a></i>;<br/>

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


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