Consider the following premises. forall y: U_1(y) -> S_1(y). forall y: P(y) -> T_3(y). exists y: T_3(y) -> U_1(y). forall y: W(y) -> P(y). Can we infer exists y: W(y) -> S_1(y) from them? If possible, name the inference rules being used at each step.
 From forall y: W(y) -> P(y), forall y: P(y) -> T_3(y) we can infer forall y: W(y) -> T_3(y) via universal transitivity. From exists y: T_3(y) -> U_1(y), forall y: U_1(y) -> S_1(y) we can infer exists y: T_3(y) -> S_1(y) via existential transitivity. Finally, from forall y: W(y) -> T_3(y), exists y: T_3(y) -> S_1(y) we can infer exists y: W(y) -> S_1(y) via existential transitivity. Therefore, the answer is yes.