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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">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>



<b>assume </b><a NAME="E1:29"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ordinal2.html#K2" target="_self">inf</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:29"/><b>then </b><i><font color="Green">E6</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K3">On</a> <font color="Maroon">X</font></span>)</span>
 
;<br/>
<b>consider </b><font color="Maroon">y</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="ordinal1.html#K3">On</a> <font color="Maroon">X</font>;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as   <a href="ordinal1.html#NM2">Ordinal</a> <b>by </b><i>, <a class="ref" href="ordinal1.html#D10">ORDINAL1:def 10</a>, <a class="ref" href="setfam_1.html#T2">SETFAM_1:2</a></i>;<br/>
<a NAME="E5:29"/>
 <a href="ordinal1.html#K3">On</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="ordinal2.html#K3" target="_self">sup</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:29"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="ordinal2.html#K3" target="_self">sup</a> <font color="Maroon">X</font>
 
<b>by </b><i>, <a class="ref" href="setfam_1.html#T2">SETFAM_1:2</a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E7:29"/><b>then </b>
( <font color="Maroon">y</font> <a href="ordinal1.html#R1">c=</a>  <a href="ordinal2.html#K3" target="_self">sup</a> <font color="Maroon">X</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> )
 
<b>by </b><i>, <a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a>, <a class="ref" href="setfam_1.html#T2">SETFAM_1:2</a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E8:29"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ordinal2.html#K3" target="_self">sup</a> <font color="Maroon">X</font>
 ;<br/>


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