Consider the following premises. forall y: U_3(y) -> Q(y). forall y: ~P(y). forall y: Q(y) <-> U_3(y). forall y: P(y) <-> U_3(y). Can we infer forall y: ~Q(y) from them? If possible, name the inference rules being used at each step.
 From forall y: Q(y) <-> U_3(y) we can infer forall y: Q(y) -> U_3(y) via universal biconditional elimination. From forall y: P(y) <-> U_3(y), forall y: ~P(y) we can infer forall y: ~U_3(y) via universal biconditional elimination. From forall y: U_3(y) -> Q(y), forall y: Q(y) -> U_3(y) we can infer forall y: U_3(y) <-> Q(y) via universal biconditional introduction. Finally, from forall y: U_3(y) <-> Q(y), forall y: ~U_3(y) we can infer forall y: ~Q(y) via universal biconditional elimination. Therefore, the answer is yes.