Consider the following premises. forall y: R_4(y) -> W(y). forall y: S(y) <-> R_4(y). forall y: W(y) -> S(y). Can we infer forall y: R_4(y) <-> W(y) from them? If possible, name the inference rules being used at each step.
 From forall y: S(y) <-> R_4(y) we can infer forall y: S(y) -> R_4(y) via universal biconditional elimination. From forall y: W(y) -> S(y), forall y: S(y) -> R_4(y) we can infer forall y: W(y) -> R_4(y) via universal transitivity. Finally, from forall y: R_4(y) -> W(y), forall y: W(y) -> R_4(y) we can infer forall y: R_4(y) <-> W(y) via universal biconditional introduction. Therefore, the answer is yes.