Consider the following premises. exists y: ~P(y). forall y: W(y) <-> W_3(y). forall y: P(y) <-> W(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: P(y) <-> W(y), exists y: ~P(y) we can infer exists y: ~W(y) via existential biconditional elimination. From forall y: W(y) <-> W_3(y) we can infer forall y: W_3(y) -> W(y) via universal biconditional elimination. Finally, from forall y: W_3(y) -> W(y), exists y: ~W(y) we can infer exists y: ~W_3(y) via existential modus tollens, which contradicts forall y: W_3(y). Therefore, the answer is no.