Consider the following premises. forall y: W_4(y) -> W(y). forall y: U(y) or ~W(y). forall y: U(y) -> W_4(y). Can we infer forall y: W_4(y) -> U(y) from them? If possible, name the inference rules being used at each step.
 From forall y: U(y) or ~W(y) we can infer forall y: W(y) -> U(y) via universal rewriting. Finally, from forall y: W_4(y) -> W(y), forall y: W(y) -> U(y) we can infer forall y: W_4(y) -> U(y) via universal transitivity. Therefore, the answer is yes.