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