Consider the following premises. forall y: T_1(y) -> U(y). forall y: U(y) -> W(y). forall y: T_1(y). Can we infer forall y: W(y) from them? If possible, name the inference rules being used at each step.
 From forall y: T_1(y) -> U(y), forall y: T_1(y) we can infer forall y: U(y) via universal modus ponens. Finally, from forall y: U(y) -> W(y), forall y: U(y) we can infer forall y: W(y) via universal modus ponens. Therefore, the answer is yes.