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