Consider the following premises. exists y: R(y) -> Q_3(y). forall y: Q_3(y) -> P(y). forall y: R(y) <-> P(y). Can we infer exists y: R(y) <-> P(y) from them?
 From exists y: R(y) -> Q_3(y), forall y: Q_3(y) -> P(y) we can infer exists y: R(y) -> P(y). From forall y: R(y) <-> P(y) we can infer forall y: P(y) -> R(y). Finally, from exists y: R(y) -> P(y), forall y: P(y) -> R(y) we can infer exists y: R(y) <-> P(y). Therefore, the answer is yes.