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