1 (a) If , and , then .
(b) If , and , then .
(c) If , and , then .
(d) If , then .
(1) If and , then their product is in .
(2) , for all .
(3) for all .
(4) contains an element , such that for every .
(5) If and , then there exists an element such that .
So (c) and (d) follows from Axiom (5), and (b) follows from Axiom (2). How about (a)?