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<b>let </b><font color="Maroon" title="c1">M</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">M</font> is <a href="card_1.html#V1" title="CARD_1:attr.1">cardinal</a> implies <font color="Maroon" title="c1">M</font> is <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a> )</span><br/>

<b>assume </b><a NAME="E1:5_1_1"/>
<font color="Maroon" title="c1">M</font> is <a href="card_1.html#V1" title="CARD_1:attr.1">cardinal</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">M</font> is <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a></span><br/>

<a NAME="E2:5_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">B</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <br/>( <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">B</font> &amp; ( for <font color="Olive" title="b2">A</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b2">A</font>,<font color="Olive" title="b1">B</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  holds <br/><font color="Olive" title="b1">B</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b2">A</font> ) )
 
<b>by </b><i><a class="ref" href="card_1.html#D1" target="_self" title="CARD_1:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E3:5_1_1"/>
<font color="Maroon" title="c1">M</font> is <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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