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<b>let </b><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font>;<br/>



<b>assume </b><a NAME="E1:64"/>
<font color="Maroon" title="c3">A</font> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>
 ;<br/>

<a NAME="E2:64"/><b>then </b>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="ref" href="tex_2.html#T5" title="TEX_2:th.5">TEX_2:5</a></i>;<br/>
<a NAME="E3:64"/><b>then </b>
(  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c3">A</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a> <font color="Maroon" title="c2">X</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D8" title="XBOOLE_0:def.8">XBOOLE_0:def 8</a>, <a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<b>hence </b><a NAME="E4:64"/>
not <font color="Maroon" title="c2">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="xboole_1.html#T59" title="XBOOLE_1:th.59">XBOOLE_1:59</a></i>;<br/>


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