Consider the following premises. forall y: T_4(y) -> S(y). forall y: U(y) -> S_2(y). forall y: S_2(y) -> T_4(y). exists y: S(y) -> U(y). Can we infer exists y: S_2(y) <-> S(y) from them? If possible, name the inference rules being used at each step.
 From exists y: S(y) -> U(y), forall y: U(y) -> S_2(y) we can infer exists y: S(y) -> S_2(y) via existential transitivity. From forall y: S_2(y) -> T_4(y), forall y: T_4(y) -> S(y) we can infer forall y: S_2(y) -> S(y) via universal transitivity. Finally, from forall y: S_2(y) -> S(y), exists y: S(y) -> S_2(y) we can infer exists y: S_2(y) <-> S(y) via existential biconditional introduction. Therefore, the answer is yes.