Consider the following premises. forall x: U_4(x) <-> W_2(x). forall x: ~U_4(x). forall x: U(x) -> W_2(x). Can we infer forall x: ~U(x) from them? If possible, name the inference rules being used at each step.
 From forall x: U_4(x) <-> W_2(x), forall x: ~U_4(x) we can infer forall x: ~W_2(x) via universal biconditional elimination. Finally, from forall x: U(x) -> W_2(x), forall x: ~W_2(x) we can infer forall x: ~U(x) via universal modus tollens. Therefore, the answer is yes.