thus for w being Element of RAT holds addrat . z,w = w :: according to BINOP_1:def 7,BINOP_1:def 16 :: thesis: z is_a_right_unity_wrt addrat

proof

let w be Element of RAT ; :: thesis: addrat . z,w = w
thus addrat . z,w = 0 + w by Def15
.= w ; :: thesis: verum

end;

let w be Element of RAT ; :: according to BINOP_1:def 17 :: thesis: addrat . w,z = w
thus addrat . w,z = w + 0 by Def15
.= w ; :: thesis: verum