let D be non empty set ; :: thesis: for p1, p2 being Element of D st p1 <> p2 holds
<*p1,p2*> -: p2 = <*p1,p2*>
let p1, p2 be Element of D; :: thesis: ( p1 <> p2 implies <*p1,p2*> -: p2 = <*p1,p2*> )
assume A1: p1 <> p2 ; :: thesis: <*p1,p2*> -: p2 = <*p1,p2*>
rng <*p1,p2*> = {p1,p2} by Lm1;
then p2 in rng <*p1,p2*> by TARSKI:def 2;
hence <*p1,p2*> -: p2 = (<*p1,p2*> -| p2) ^ <*p2*> by Th40
.= <*p1,p2*> by A1, Th26 ;
:: thesis: verum