let D be non empty set ; :: thesis: for p1, p2, p3 being Element of D st p1 <> p3 & p2 <> p3 holds
<*p1,p2,p3*> -: p3 = <*p1,p2,p3*>
let p1, p2, p3 be Element of D; :: thesis: ( p1 <> p3 & p2 <> p3 implies <*p1,p2,p3*> -: p3 = <*p1,p2,p3*> )
assume that
A1: p1 <> p3 and
A2: p2 <> p3 ; :: thesis: <*p1,p2,p3*> -: p3 = <*p1,p2,p3*>
rng <*p1,p2,p3*> = {p1,p2,p3} by Lm2;
then p3 in rng <*p1,p2,p3*> by ENUMSET1:def 1;
hence <*p1,p2,p3*> -: p3 = (<*p1,p2,p3*> -| p3) ^ <*p3*> by Th40
.= <*p1,p2*> ^ <*p3*> by A1, A2, Th28
.= <*p1,p2,p3*> ;
:: thesis: verum