Consider the following premises. forall y: ~S(y). forall y: T(y) <-> S(y). forall y: S(y) -> T(y). exists y: W_4(y) -> T(y). Can we infer exists y: ~W_4(y) from them? If possible, name the inference rules being used at each step.
 From forall y: T(y) <-> S(y) we can infer forall y: T(y) -> S(y) via universal biconditional elimination. From forall y: T(y) -> S(y), forall y: S(y) -> T(y) we can infer forall y: T(y) <-> S(y) via universal biconditional introduction. From forall y: T(y) <-> S(y), forall y: ~S(y) we can infer forall y: ~T(y) via universal biconditional elimination. Finally, from exists y: W_4(y) -> T(y), forall y: ~T(y) we can infer exists y: ~W_4(y) via existential modus tollens. Therefore, the answer is yes.