Consider the following premises. forall y: P(y) -> W(y). forall y: W(y) -> P(y). forall y: P(y) or ~Q_3(y). exists y: Q_3(y). Can we infer exists y: W(y) from them? If possible, name the inference rules being used at each step.
 From forall y: P(y) or ~Q_3(y) we can infer forall y: Q_3(y) -> P(y) via universal rewriting. From forall y: W(y) -> P(y), forall y: P(y) -> W(y) we can infer forall y: W(y) <-> P(y) via universal biconditional introduction. From forall y: W(y) <-> P(y) we can infer forall y: P(y) -> W(y) via universal biconditional elimination. From forall y: Q_3(y) -> P(y), exists y: Q_3(y) we can infer exists y: P(y) via existential modus ponens. Finally, from forall y: P(y) -> W(y), exists y: P(y) we can infer exists y: W(y) via existential modus ponens. Therefore, the answer is yes.