Consider the following premises. exists y: Q_2(y). forall y: R_2(y) <-> Q_2(y). forall y: Q(y). Can we infer exists y: R_2(y) from them?
 From exists y: Q_2(y), forall y: Q(y) we can infer exists y: Q_2(y) and Q(y). From forall y: R_2(y) <-> Q_2(y) we can infer forall y: Q_2(y) -> R_2(y). From exists y: Q_2(y) and Q(y) we can infer exists y: Q_2(y). Finally, from forall y: Q_2(y) -> R_2(y), exists y: Q_2(y) we can infer exists y: R_2(y). Therefore, the answer is yes.