Consider the following premises. forall y: Q_3(y) <-> P(y). exists y: P(y). forall y: Q_3(y) -> W(y). Can we infer forall y: ~W(y) from them? If possible, name the inference rules being used at each step.
 From forall y: Q_3(y) <-> P(y) we can infer forall y: P(y) -> Q_3(y) via universal biconditional elimination. From forall y: P(y) -> Q_3(y), forall y: Q_3(y) -> W(y) we can infer forall y: P(y) -> W(y) via universal transitivity. Finally, from forall y: P(y) -> W(y), exists y: P(y) we can infer exists y: W(y) via existential modus ponens, which contradicts forall y: ~W(y). Therefore, the answer is no.