Consider the following premises. forall z: T(z) -> T_3(z). forall z: T_3(z) -> Q(z). exists z: Q(z) -> T(z). forall z: Q(z) -> T_3(z). Can we infer forall z: Q(z) -> T_3(z) from them?
That is one of the premises. Therefore, the answer is yes.