let C, D be non empty set ; :: thesis:
let e be Element of D; :: thesis:
let f be Function of C,D; :: thesis:
let F, G be BinOp of D; :: thesis:
reconsider g = C --> e as Function of C,D ;
assume A1: ( F is associative & F is having_a_unity & e = the_unity_wrt F & F is having_an_inverseOp & G is_distributive_wrt F ) ; :: thesis:

let c be Element of C; :: thesis:
thus (G [;] (e,f)) . c = G . (e,(f . c)) by FUNCOP_1:53
.= e by A1, Th66
.= g . c ; :: thesis:

end;