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<span class="kw">set </span><font color="Maroon" title="c3">x</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>;<br/>
<a NAME="E1:143_1_1"/>
(  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> implies  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"> the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Olive" title="b1">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D14" target="_self" onmouseover="rs('relat_1/D14')" onmouseout="rh()">Def12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:143_1_1"/>
<font color="Maroon" title="c1">R</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <font color="Maroon" title="c2">Y</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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