Consider the following premises. t_4 <-> S(f). T(f) -> t_4. forall x: T(x) <-> S(x). Can we infer S(f) <-> t_4 from them? If possible, name the inference rules being used at each step.
 From forall x: T(x) <-> S(x) we can infer forall x: S(x) -> T(x) via universal biconditional elimination. From forall x: S(x) -> T(x) we can infer S(f) -> T(f) via universal instantiation. From S(f) -> T(f), T(f) -> t_4 we can infer S(f) -> t_4 via transitivity. From t_4 <-> S(f) we can infer t_4 -> S(f) via biconditional elimination. Finally, from S(f) -> t_4, t_4 -> S(f) we can infer S(f) <-> t_4 via biconditional introduction. Therefore, the answer is yes.