Consider the following premises. forall x: ~U(x). q <-> W_3(e). forall x: W_3(x) -> U(x). forall x: U(x) -> W_3(x). Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From forall x: W_3(x) -> U(x), forall x: U(x) -> W_3(x) we can infer forall x: W_3(x) <-> U(x) via universal biconditional introduction. From forall x: W_3(x) <-> U(x), forall x: ~U(x) we can infer forall x: ~W_3(x) via universal biconditional elimination. From forall x: ~W_3(x) we can infer ~W_3(e) via universal instantiation. Finally, from q <-> W_3(e), ~W_3(e) we can infer ~q via biconditional elimination. Therefore, the answer is yes.