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

<b>assume </b><a NAME="E1:45"/>
 <a href="ordinal1.html#K5">omega</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="ordinal4.html#M1">Ordinal</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>3</sub></font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:45"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="zfrefle1.html#R4" target="_self">is_cofinal_with</a>  <a href="ordinal1.html#K5">omega</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="classes1.html#K4">Rank</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="zfrefle1.html#R3" target="_self">is_elementary_subsystem_of</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="zfrefle1.html#T37" target="_self">Th37</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E4:45"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="zfrefle1.html#R4" target="_self">is_cofinal_with</a>  <a href="ordinal1.html#K5">omega</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="classes1.html#K4">Rank</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="zfrefle1.html#R2" target="_self">&lt;==&gt;</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="zfrefle1.html#E3:45"><i><font color="Green">E28</font></i></a>, <a class="ref" href="zfrefle1.html#T9" target="_self">Th9</a></i>;<br/>


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