Could someone please tell me if my proof is correct

Suppose f: A B and q: BC are both injective.. ( 0 ) Prove gof: Ac is injective. Suppose f:A - B is injective, Then Va, a'cA IGEB, Then fla)= f(a') # and a = a Likewise, Suppose q: 8 - C is injective, Then Vb, b'E B, Then g (6) = 9(6') and 6=6. Since fla) = f (a'), Then q(f (a)) = g (f(a')), which means gof(a) = q of ( a'). Since gofla) = gof (a') and a=a' Then got is injective