Consider the following premises. exists y: S(y) -> T_3(y). forall y: S(y) <-> T_3(y). forall y: ~T_3(y). Can we infer forall y: S(y) from them? If possible, name the inference rules being used at each step.
 From forall y: S(y) <-> T_3(y) we can infer forall y: T_3(y) -> S(y) via universal biconditional elimination. From forall y: T_3(y) -> S(y), exists y: S(y) -> T_3(y) we can infer exists y: T_3(y) <-> S(y) via existential biconditional introduction. Finally, from exists y: T_3(y) <-> S(y), forall y: ~T_3(y) we can infer exists y: ~S(y) via existential biconditional elimination, which contradicts forall y: S(y). Therefore, the answer is no.