Consider the following premises. exists y: S(y) -> Q_1(y). forall y: S(y) or ~P(y). forall y: S(y) -> P(y). Can we infer exists y: P(y) -> Q_1(y) from them?
 From forall y: S(y) or ~P(y) we can infer forall y: P(y) -> S(y). From forall y: S(y) -> P(y), forall y: P(y) -> S(y) we can infer forall y: S(y) <-> P(y). From forall y: S(y) <-> P(y) we can infer forall y: P(y) -> S(y). Finally, from forall y: P(y) -> S(y), exists y: S(y) -> Q_1(y) we can infer exists y: P(y) -> Q_1(y). Therefore, the answer is yes.