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<b>let </b><font color="Maroon" title="c1">W</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font> be    <a href="ordinal4.html#M1" title="ORDINAL4:mode.1">Ordinal</a> of <font color="Maroon" title="c1">W</font>;<br/>



<b>given </b><font color="Maroon" title="c3">psi</font> being   <a href="ordinal2.html#NM1" title="ORDINAL2:NM.1">Ordinal-Sequence</a><b> such that </b><a NAME="E2:25"/><i><font color="Green" title="E17">A1</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">psi</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c1">W</font> &amp; <font color="Maroon" title="c3">psi</font> is <a href="ordinal2.html#V2" title="ORDINAL2:attr.2">increasing</a> &amp;  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal2.html#K4" title="ORDINAL2:func.4">sup</a> <font color="Maroon" title="c3">psi</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ordinal2.html#D21" title="ORDINAL2:def.21">ORDINAL2:def 21</a><br/>

<a NAME="E3:25"/>
 <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c1">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">W</font>
 
<b>by </b><i><a class="ref" href="ordinal2.html#T9" title="ORDINAL2:th.9">ORDINAL2:9</a></i>;<br/>
<a NAME="E4:25"/><b>then </b>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">psi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">psi</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">W</font> )
 
<b>by </b><i><a class="txt" href="zfrefle1.html#E2:25"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="ordinal4.html#D2" title="ORDINAL4:def.2">ORDINAL4:def 2</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:25"/><b>then </b>
 <a href="ordinal2.html#K3" title="ORDINAL2:func.3">sup</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">psi</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font>
 
<b>by </b><i><a class="ref" href="zfrefle1.html#T12" target="_self" title="ZFREFLE1:th.12">Th12</a>, <a class="ref" href="zf_refle.html#T28" title="ZF_REFLE:th.28">ZF_REFLE:28</a></i>;<br/>
<a NAME="E6:25"/><b>then </b>
 <a href="ordinal2.html#K4" title="ORDINAL2:func.4">sup</a> <font color="Maroon" title="c3">psi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <font color="Maroon" title="c1">W</font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#D10" title="ORDINAL1:def.10">ORDINAL1:def 10</a></i>;<br/>
<b>hence </b><a NAME="E7:25"/>
contradiction
 <b>by </b><i><a class="txt" href="zfrefle1.html#E2:25"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>


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