Consider the following premises. exists y: S_2(y) or ~Q(y). forall y: S_2(y) <-> Q(y). Can we infer exists y: Q(y) -> S_2(y) from them? If possible, name the inference rules being used at each step.
 From forall y: S_2(y) <-> Q(y) we can infer forall y: S_2(y) -> Q(y) via universal biconditional elimination. Finally, from exists y: S_2(y) or ~Q(y) we can infer exists y: Q(y) -> S_2(y) via existential rewriting. Therefore, the answer is yes.