Consider the following premises. forall z: U(z) -> T(z). forall z: S_2(z) <-> T(z). Can we infer forall z: U(z) -> S_2(z) from them? If possible, name the inference rules being used at each step.
 From forall z: S_2(z) <-> T(z) we can infer forall z: T(z) -> S_2(z) via universal biconditional elimination. Finally, from forall z: U(z) -> T(z), forall z: T(z) -> S_2(z) we can infer forall z: U(z) -> S_2(z) via universal transitivity. Therefore, the answer is yes.