let D be non empty set ; :: thesis: for p1, p3, p2 being Element of D st p1 <> p3 & p2 <> p3 holds
<*p1,p2,p3*> -: p3 = <*p1,p2,p3*>
let p1, p3, p2 be Element of D; :: thesis: ( p1 <> p3 & p2 <> p3 implies <*p1,p2,p3*> -: p3 = <*p1,p2,p3*> )
assume A1: ( p1 <> p3 & 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 Th44
.= <*p1,p2*> ^ <*p3*> by A1, Th32
.= <*p1,p2,p3*> by FINSEQ_1:60 ;
:: thesis: verum