let D be non empty set ; :: thesis: for p1, p2, p3 being Element of D st p1 <> p2 holds
<*p1,p2,p3*> :- p2 = <*p2,p3*>
let p1, p2, p3 be Element of D; :: thesis: ( p1 <> p2 implies <*p1,p2,p3*> :- p2 = <*p2,p3*> )
assume A1: p1 <> p2 ; :: thesis: <*p1,p2,p3*> :- p2 = <*p2,p3*>
p2 in {p1,p2,p3} by ENUMSET1:def 1;
then p2 in rng <*p1,p2,p3*> by Lm2;
hence <*p1,p2,p3*> :- p2 = <*p2*> ^ (<*p1,p2,p3*> |-- p2) by Th41
.= <*p2,p3*> by A1, Th30 ;
:: thesis: verum