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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">psi</font> be   <a href="ordinal2.html#NM1">Ordinal-Sequence</a>;<br/>



<b>consider </b><font color="Maroon">A</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E2:18"/><i><font color="Green">E31</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">psi</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="ordinal2.html#D8">ORDINAL2:def 8</a></i>;<br/>
<a NAME="E3:18"/><i><font color="Green">E37</font></i>: 
(  <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">psi</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">psi</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">psi</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">psi</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T118">RELAT_1:118</a>, <a class="ref" href="card_3.html#D4">CARD_3:def 4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:18_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">psi</font></span>)</span>
 ;<br/><a NAME="E2:18_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><b>hence </b><a NAME="E3:18_1"/>
<font color="Maroon">x</font> is   <a href="ordinal1.html#NM2">Ordinal</a>
 <b>by </b><i><a class="ref" href="ordinal1.html#T23">ORDINAL1:23</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:18"/>
 <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">psi</font></span>)</span> is   <a href="ordinal1.html#NM2">Ordinal</a>
 <b>by </b><i>, <a class="ref" href="ordinal1.html#T35">ORDINAL1:35</a></i>;<br/>


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