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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">R</font> be   <a href="relset_1.html#NM3" title="RELSET_1:NM.3">Relation</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c2">R</font> <a href="relat_2.html#R2" title="RELAT_2:pred.2">is_irreflexive_in</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<a NAME="E2:17"/>
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c2">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T19" title="RELSET_1:th.19">RELSET_1:19</a></i>;<br/>
<a NAME="E3:17"/><b>then </b>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c2">R</font> holds <br/> not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b1">x</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="c2">R</font>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E1:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="relat_2.html#D2" title="RELAT_2:def.2">RELAT_2:def 2</a></i>;<br/>
<a NAME="E4:17"/><b>then </b>
<font color="Maroon" title="c2">R</font> <a href="relat_2.html#R2" title="RELAT_2:pred.2">is_irreflexive_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c2">R</font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D2" title="RELAT_2:def.2">RELAT_2:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:17"/>
<font color="Maroon" title="c2">R</font> is <a href="relat_2.html#V2" title="RELAT_2:attr.2">irreflexive</a>
 <b>by </b><i><a class="ref" href="relat_2.html#D10" title="RELAT_2:def.10">RELAT_2:def 10</a></i>;<br/>


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