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<b>let </b><font color="Maroon" title="c2">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>;<br/>

<b>assume </b><a NAME="E1:20_1_1"/>
<font color="Maroon" title="c2">A</font> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>
 ;<br/>

<a NAME="E2:20_1_1"/><b>then </b><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="ref" href="tex_2.html#T5" target="_self" title="TEX_2:th.5">Th5</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">s</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Y</font><b> such that </b><br/><a NAME="E4:20_1_1"/><i><font color="Green" title="E7">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">s</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="tex_1.html#D1" title="TEX_1:def.1">TEX_1:def 1</a></i>;<br/>
<b>thus </b><a NAME="E5:20_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_2.html#E2:20_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="tex_2.html#E4:20_1_1"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T39" title="ZFMISC_1:th.39">ZFMISC_1:39</a></i>;<br/>


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