Consider the following premises. exists y: S(y) -> T(y). forall y: S(y) or ~W(y). forall y: T(y) -> W(y). Can we infer exists y: W(y) <-> T(y) from them?
 From forall y: S(y) or ~W(y) we can infer forall y: W(y) -> S(y). From forall y: W(y) -> S(y), exists y: S(y) -> T(y) we can infer exists y: W(y) -> T(y). Finally, from exists y: W(y) -> T(y), forall y: T(y) -> W(y) we can infer exists y: W(y) <-> T(y). Therefore, the answer is yes.