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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="relset_1.html#NM3">Relation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:17"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R2">is_irreflexive_in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:17"/>
 <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T19">RELSET_1:19</a></i>;<br/>
<a NAME="E3:17"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> holds <br/> not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E1:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="relat_2.html#D2">RELAT_2:def 2</a></i>;<br/>
<a NAME="E4:17"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R2">is_irreflexive_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D2">RELAT_2:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:17"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="relat_2.html#V2">irreflexive</a>
 <b>by </b><i><a class="ref" href="relat_2.html#D10">RELAT_2:def 10</a></i>;<br/>


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