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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:4"/><i><font color="Green">E5</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is  <a href="card_1.html#V1">cardinal</a>  <a href="ordinal1.html#NM1" target="_self">number</a> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:4_1"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:4_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is  <a href="card_1.html#V1">cardinal</a>  <a href="ordinal1.html#NM1" target="_self">number</a> 
 <b>by </b><i><a class="txt" href="topgen_2.html#E1:4"><i><font color="Green">E5</font></i></a></i>;<br/><b>hence </b><a NAME="E3:4_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="card_1.html#V1">cardinal</a>  <a href="hidden.html#M1">set</a>  )
 <b>by </b><i><a class="txt" href="topgen_2.html#E1:4_1"><i><font color="Green">E6</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:4"/>
 <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>1</sub></font> is  <a href="card_1.html#V1">cardinal</a>  <a href="ordinal1.html#NM1" target="_self">number</a> 
 <b>by </b><i><a class="ref" href="card_lar.html#T33">CARD_LAR:33</a></i>;<br/>


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