Consider the following premises. forall x: ~Q(x). forall x: U(x) <-> Q(x). forall x: Q(x) -> U(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(x) <-> Q(x) we can infer forall x: U(x) -> Q(x) via universal biconditional elimination. From forall x: Q(x) -> U(x), forall x: U(x) -> Q(x) we can infer forall x: Q(x) <-> U(x) via universal biconditional introduction. Finally, from forall x: Q(x) <-> U(x), forall x: ~Q(x) we can infer forall x: ~U(x) via universal biconditional elimination. Therefore, the answer is yes.