Consider the following premises. forall y: S(y) -> U(y). forall y: P(y) -> Q(y). forall y: Q_3(y) -> S(y). exists y: U(y) -> P(y). Can we infer exists y: Q_3(y) -> Q(y) from them? If possible, name the inference rules being used at each step.
 From forall y: S(y) -> U(y), exists y: U(y) -> P(y) we can infer exists y: S(y) -> P(y) via existential transitivity. From forall y: Q_3(y) -> S(y), exists y: S(y) -> P(y) we can infer exists y: Q_3(y) -> P(y) via existential transitivity. Finally, from exists y: Q_3(y) -> P(y), forall y: P(y) -> Q(y) we can infer exists y: Q_3(y) -> Q(y) via existential transitivity. Therefore, the answer is yes.