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