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 = <*p3*>
let p1, p2, p3 be Element of D; :: thesis: ( p1 <> p3 & p2 <> p3 implies <*p1,p2,p3*> :- p3 = <*p3*> )
assume that
A1: p1 <> p3 and
A2: p2 <> p3 ; :: thesis: <*p1,p2,p3*> :- p3 = <*p3*>
p3 in {p1,p2,p3} by ENUMSET1:def 1;
then p3 in rng <*p1,p2,p3*> by Lm2;
hence <*p1,p2,p3*> :- p3 = <*p3*> ^ (<*p1,p2,p3*> |-- p3) by Th41
.= <*p3*> ^ {} by A1, A2, Th34
.= <*p3*> by FINSEQ_1:34 ;
:: thesis: verum