Consider the following premises. forall z_3: R(z_3) or ~U(z_3). forall z_3: T_4(z_3) -> U(z_3). forall z_3: R(z_3) <-> T_4(z_3). Can we infer forall z_3: U(z_3) -> T_4(z_3) from them? If possible, name the inference rules being used at each step.
 From forall z_3: R(z_3) or ~U(z_3) we can infer forall z_3: U(z_3) -> R(z_3) via universal rewriting. From forall z_3: R(z_3) <-> T_4(z_3) we can infer forall z_3: R(z_3) -> T_4(z_3) via universal biconditional elimination. Finally, from forall z_3: U(z_3) -> R(z_3), forall z_3: R(z_3) -> T_4(z_3) we can infer forall z_3: U(z_3) -> T_4(z_3) via universal transitivity. Therefore, the answer is yes.