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<b>assume </b><a NAME="E1:96"/>
 <a href="newton.html#K14" target="_self">SetPrimenumber</a> 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:96"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K14" target="_self">SetPrimenumber</a> 2
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i>, <a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E5:96"/>
( <font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 &amp; <font color="Maroon">x</font> is <a href="int_2.html#V1">prime</a> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:96"/><b>then </b>
( 0 is <a href="int_2.html#V1">prime</a> or 1 is <a href="int_2.html#V1">prime</a> )
 
<b>by </b><i><a class="ref" href="cqc_the1.html#T3">CQC_THE1:3</a></i>;<br/>
<b>hence </b><a NAME="E7:96"/>
contradiction
 <b>by </b><i><a class="ref" href="int_2.html#D5">INT_2:def 5</a></i>;<br/>


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