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