Consider the following premises. forall y: Q(y) -> U(y). forall y: Q(y) -> P(y). forall y: P(y) -> Q(y). Can we infer forall y: P(y) -> U(y) from them? If possible, name the inference rules being used at each step.
 From forall y: Q(y) -> P(y), forall y: P(y) -> Q(y) we can infer forall y: Q(y) <-> P(y) via universal biconditional introduction. From forall y: Q(y) <-> P(y) we can infer forall y: P(y) -> Q(y) via universal biconditional elimination. Finally, from forall y: P(y) -> Q(y), forall y: Q(y) -> U(y) we can infer forall y: P(y) -> U(y) via universal transitivity. Therefore, the answer is yes.