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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM2">Ordinal</a>] <b>means </b> <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font>;<br/>
<a NAME="E1:25"/><i><font color="Green">E25</font></i>: 
 ex <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">A</font>]
 
<b>by </b><i><a class="ref" href="classes1.html#D1" target="_self">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon">A</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E3:25"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">A</font>] &amp; ( for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">B</font>] holds <br/><font color="Maroon">A</font> <a href="ordinal1.html#R1">c=</a> <font color="Olive">B</font> ) )
 <b>from </b><i><a class="ref" href="ordinal1.html#S1">ORDINAL1:sch 1</a>(<a class="ref" href="classes1.html#D2" target="_self">Def2</a>);<br/></i>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<b>thus </b><a NAME="E4:25"/>
 <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">B</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>

<b>assume </b><a NAME="E5:25"/>
<font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E6:25"/><b>then </b>
not <font color="Maroon">A</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#T7">ORDINAL1:7</a></i>;<br/>
<b>hence </b><a NAME="E7:25"/>
 <a href="classes1.html#K3" target="_self">Tarski-Class</a> <font color="Maroon">X</font>,<font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>


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