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<a NAME="E1:9_1"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  ex <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">d</font>,<font color="Olive">A</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>();<br/>

<b>consider </b><font color="Maroon">a</font> being    <a href="ordinal4.html#M1">Ordinal</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E2:9_1_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">d</font>,<font color="Maroon">a</font>]
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a</font> as   <a href="ordinal1.html#NM2">Ordinal</a> ;<br/>
<b>take </b>
<font color="Maroon">a</font>
;<br/>

<b>thus </b><a NAME="E4:9_1_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">d</font>,<font color="Maroon">a</font>]
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">F</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E3:9_1"/><i><font color="Green">E53</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>()
 <b>and </b><br/><a NAME="E4:9_1"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  ex <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">d</font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">d</font>,<font color="Olive">A</font>] &amp; ( for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">d</font>,<font color="Olive">B</font>] holds <br/><font color="Olive">A</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> ) )
 <b>from </b><i><a class="ref" href="zf_refle.html#S1" target="_self">ZF_REFLE:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon">F</font>
;<br/>

<b>thus </b><a NAME="E5:9_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>()
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>();<br/>

<b>consider </b><font color="Maroon">A</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E7:9_1"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">d</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">P<sub>1</sub></font>[<font color="Maroon">d</font>,<font color="Olive">B</font>] holds <br/><font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> ) )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">a</font> being    <a href="ordinal4.html#M1">Ordinal</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E9:9_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">d</font>,<font color="Maroon">a</font>]
 <b>by </b><i/>;<br/>
<a NAME="E10:9_1"/>
( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() )
 
<b>by </b><i>, , <a class="ref" href="ordinal4.html#D2">ORDINAL4:def 2</a></i>;<br/>
<a NAME="E11:9_1"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i><a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">A</font> as    <a href="ordinal4.html#M1">Ordinal</a> of <font color="Maroon">F<sub>1</sub></font>() <b>by </b><i><a class="ref" href="ordinal4.html#D2">ORDINAL4:def 2</a></i>;<br/>
<b>take </b>
<font color="Maroon">a</font>
;<br/>

<b>thus </b><a NAME="E13:9_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">d</font>,<font color="Maroon">a</font>] &amp; ( for <font color="Olive">b</font> being   <a href="ordinal4.html#M1">Ordinal</a> of <font color="Maroon">F<sub>1</sub></font>()  st <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">d</font>,<font color="Olive">b</font>] holds <br/><font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">b</font> ) )
 <b>by </b><i/>;<br/>


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