Consider the following premises. forall y_2: Q_4(y_2) -> P(y_2). forall y_2: ~P(y_2). exists y_2: P(y_2) <-> Q_4(y_2). Can we infer exists y_2: ~Q_4(y_2) from them? If possible, name the inference rules being used at each step.
 From exists y_2: P(y_2) <-> Q_4(y_2) we can infer exists y_2: P(y_2) -> Q_4(y_2) via existential biconditional elimination. From forall y_2: Q_4(y_2) -> P(y_2), exists y_2: P(y_2) -> Q_4(y_2) we can infer exists y_2: Q_4(y_2) <-> P(y_2) via existential biconditional introduction. Finally, from exists y_2: Q_4(y_2) <-> P(y_2), forall y_2: ~P(y_2) we can infer exists y_2: ~Q_4(y_2) via existential biconditional elimination. Therefore, the answer is yes.