<?xml version="1.0"?>
<div class="add">

<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>let </b><font color="Maroon" title="c3">phi</font> be    <a href="ordinal4.html#M2" title="ORDINAL4:mode.2">Ordinal-Sequence</a> of <font color="Maroon" title="c1">W</font>;<br/>





<a NAME="E1:22"/>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">phi</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;  <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>, <a class="ref" href="ordinal4.html#D3" title="ORDINAL4:def.3">ORDINAL4:def 3</a></i>;<br/>
<a NAME="E2:22"/><b>then </b>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">phi</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">phi</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">phi</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="relat_1.html#T99" title="RELAT_1:th.99">RELAT_1:99</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E3:22"/><b>then </b>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">W</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">W</font> &amp; <font color="Maroon" title="c2">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="ref" href="classes1.html#T44" title="CLASSES1:th.44">CLASSES1:44</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:22"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c1">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">phi</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">a</font></span>)</span> &amp; <font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">W</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T82" title="FUNCT_1:th.82">FUNCT_1:82</a>, <a class="ref" href="relat_1.html#T125" title="RELAT_1:th.125">RELAT_1:125</a></i>;<br/>
<a NAME="E5:22"/><b>then </b>
(  <a href="zf_refle.html#K2" title="ZF_REFLE:func.2">union</a> <font color="Maroon" title="c3">phi</font>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> &amp;  <a href="zf_refle.html#K2" title="ZF_REFLE:func.2">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font></span>)</span>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font></span>)</span> )
 
;<br/>
<b>hence </b><a NAME="E6:22"/>
(  <a href="zf_refle.html#K2" title="ZF_REFLE:func.2">union</a> <font color="Maroon" title="c3">phi</font>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font></span>)</span> &amp;  <a href="zf_refle.html#K2" title="ZF_REFLE:func.2">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font></span>)</span>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">phi</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c2">a</font></span>)</span> )
 <b>by </b><i><a class="ref" href="zf_refle.html#T15" target="_self" title="ZF_REFLE:th.15">Th15</a></i>;<br/>


</div>
