Consider the following premises. forall z_1: R_1(z_1) <-> W_2(z_1). exists z_1: R_1(z_1) <-> S(z_1). Can we infer exists z_1: S(z_1) -> W_2(z_1) from them?
 From exists z_1: R_1(z_1) <-> S(z_1) we can infer exists z_1: S(z_1) -> R_1(z_1). From forall z_1: R_1(z_1) <-> W_2(z_1) we can infer forall z_1: R_1(z_1) -> W_2(z_1). Finally, from exists z_1: S(z_1) -> R_1(z_1), forall z_1: R_1(z_1) -> W_2(z_1) we can infer exists z_1: S(z_1) -> W_2(z_1). Therefore, the answer is yes.