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