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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>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<div><i><font color="Green">E30</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="53_1"><b>now </b></a><div class="add"><b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>;<br/><b>assume </b><a NAME="E2:53_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E3:53_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#D4">RELAT_1:def 4</a></i>;<br/><b>hence </b><a NAME="E4:53_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="ordinal1.html#NM3">T-Sequence</a> <b>by </b><i><a class="ref" href="ordinal1.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E4:53"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="ordinal1.html#E2:53"><i><font color="Green">E30</font></i></a>, <a class="ref" href="relat_1.html#T65">RELAT_1:65</a></i>;<br/>
<a NAME="E5:53"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<b>hence </b><a NAME="E6:53"/>
 <a href="xboole_0.html#K1">{}</a>  is    <a href="ordinal1.html#M1" target="_self">T-Sequence</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="ordinal1.html#D8" target="_self">Def8</a></i>;<br/>


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