Consider the following premises. forall z_2: Q(z_2) -> T(z_2). forall z_2: S_1(z_2) -> Q(z_2). exists z_2: T(z_2) -> S_1(z_2). Can we infer exists z_2: T(z_2) <-> Q(z_2) from them?
 From exists z_2: T(z_2) -> S_1(z_2), forall z_2: S_1(z_2) -> Q(z_2) we can infer exists z_2: T(z_2) -> Q(z_2). Finally, from exists z_2: T(z_2) -> Q(z_2), forall z_2: Q(z_2) -> T(z_2) we can infer exists z_2: T(z_2) <-> Q(z_2). Therefore, the answer is yes.