Consider the following premises. forall z_1: Q(z_1) -> T(z_1). forall z_1: U_4(z_1) -> Q(z_1). forall z_1: T(z_1) -> Q(z_1). Can we infer forall z_1: U_4(z_1) -> T(z_1) from them? If possible, name the inference rules being used at each step.
 From forall z_1: T(z_1) -> Q(z_1), forall z_1: Q(z_1) -> T(z_1) we can infer forall z_1: T(z_1) <-> Q(z_1) via universal biconditional introduction. From forall z_1: T(z_1) <-> Q(z_1) we can infer forall z_1: Q(z_1) -> T(z_1) via universal biconditional elimination. Finally, from forall z_1: U_4(z_1) -> Q(z_1), forall z_1: Q(z_1) -> T(z_1) we can infer forall z_1: U_4(z_1) -> T(z_1) via universal transitivity. Therefore, the answer is yes.