Consider the following premises. exists y: W(y). forall y: W_3(y) -> W(y). forall y: W(y) -> W_3(y). Can we infer forall y: ~W_3(y) from them? If possible, name the inference rules being used at each step.
 From forall y: W(y) -> W_3(y), forall y: W_3(y) -> W(y) we can infer forall y: W(y) <-> W_3(y) via universal biconditional introduction. From forall y: W(y) <-> W_3(y) we can infer forall y: W(y) -> W_3(y) via universal biconditional elimination. Finally, from forall y: W(y) -> W_3(y), exists y: W(y) we can infer exists y: W_3(y) via existential modus ponens, which contradicts forall y: ~W_3(y). Therefore, the answer is no.