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<b>consider </b><font color="Maroon" title="c1">A</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>] <b>means </b><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon" title="c1">A</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> ;<br/>
<a NAME="E2:3_1_1"/><i><font color="Green" title="E3">A1</font></i>: 
 ex <font color="Olive" title="b1">A</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">A</font>]
 
;<br/>
<b>consider </b><font color="Maroon" title="c2">B</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><b> such that </b><br/><a NAME="E4:3_1_1"/><i><font color="Green" title="E4">A2</font></i>: 
( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">B</font>] &amp; ( for <font color="Olive" title="b1">C</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">C</font>] holds <br/><font color="Maroon" title="c2">B</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">C</font> ) )
 <b>from </b><i><a class="ref" href="ordinal1.html#S1" title="ORDINAL1:sch.1">ORDINAL1:sch 1</a>(<a class="txt" href="card_1.html#E2:3_1_1"><i><font color="Green" title="E3">A1</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon" title="c3">IT</font> = <font color="Maroon" title="c2">B</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>take </b>
<font color="Maroon" title="c3">IT</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c2">B</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="card_1.html#D1" target="_self" title="CARD_1:def.1">CARD_1:def 1</a><br/>

<b>thus </b><a NAME="E6:3_1_1"/>
<font color="Maroon" title="c3">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">C</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/>

<b>assume </b><a NAME="E7:3_1_1"/>
<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">B</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 ;<br/>

<a NAME="E8:3_1_1"/><b>then </b>
<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c1">A</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 
<b>by </b><i><a class="txt" href="card_1.html#E4:3_1_1"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="wellord2.html#T22" title="WELLORD2:th.22">WELLORD2:22</a></i>;<br/>
<b>hence </b><a NAME="E9:3_1_1"/>
<font color="Maroon" title="c2">B</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">C</font>
 <b>by </b><i><a class="txt" href="card_1.html#E4:3_1_1"><i><font color="Green" title="E4">A2</font></i></a></i>;<br/>


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