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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">R</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/>



<b>assume </b><a NAME="E1:184"/><i><font color="Green">E31</font></i>: 
not <font color="Maroon">R</font> <a href="relat_1.html#K7" target="_self">|</a> <font color="Maroon">X</font> is <a href="relat_1.html#V3" target="_self">empty-yielding</a>
 ;<br/>

<a NAME="E2:184"/><i><font color="Green">E36</font></i>: 
 <a href="relat_1.html#K2" target="_self">rng</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relat_1.html#K7" target="_self">|</a> <font color="Maroon">X</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>assume </b><a NAME="E3:184"/>
<font color="Maroon">R</font> is <a href="relat_1.html#V3" target="_self">empty-yielding</a>
 ;<br/>

<a NAME="E4:184"/><b>then </b>
 <a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">R</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:184"/><b>then </b>
 <a href="relat_1.html#K2" target="_self">rng</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relat_1.html#K7" target="_self">|</a> <font color="Maroon">X</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="relat_1.html#D9" target="_self">Def9</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E6:184"/>
contradiction
 <b>by </b><i><a class="ref" href="relat_1.html#T66" target="_self">Th66</a>, </i>;<br/>


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