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