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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:14"/><i><font color="Green">E5</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> is <a href="tex_2.html#V1" target="_self">proper</a>
 ;<br/>

<b>assume </b><a NAME="E2:14"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="realset1.html#V1">trivial</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="realset1.html#V1">trivial</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<a NAME="E4:14"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> is  non <a href="xboole_0.html#V1">empty</a> <a href="realset1.html#V1">trivial</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>3</sub></font>
 
;<br/>
<b>hence </b><a NAME="E5:14"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_2.html#E1:14"><i><font color="Green">E5</font></i></a></i>;<br/>


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