Consider the following premises. forall y: Q(y) <-> Q_4(y). exists y: U(y) <-> Q(y). forall y: U(y) -> Q_4(y). Can we infer exists y: U(y) -> Q(y) from them?
 From forall y: Q(y) <-> Q_4(y) we can infer forall y: Q_4(y) -> Q(y). From forall y: U(y) -> Q_4(y), forall y: Q_4(y) -> Q(y) we can infer forall y: U(y) -> Q(y). From exists y: U(y) <-> Q(y) we can infer exists y: Q(y) -> U(y). From exists y: Q(y) -> U(y), forall y: U(y) -> Q(y) we can infer exists y: Q(y) <-> U(y). Finally, from exists y: Q(y) <-> U(y) we can infer exists y: U(y) -> Q(y). Therefore, the answer is yes.