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