Consider the following premises. forall x: P(x) -> Q(x). forall x: Q(x) -> W(x). forall x: W(x) -> T_1(x). forall x: T_1(x) -> P(x). Can we infer forall x: T_1(x) <-> P(x) from them? If possible, name the inference rules being used at each step.
 From forall x: Q(x) -> W(x), forall x: W(x) -> T_1(x) we can infer forall x: Q(x) -> T_1(x) via universal transitivity. From forall x: P(x) -> Q(x), forall x: Q(x) -> T_1(x) we can infer forall x: P(x) -> T_1(x) via universal transitivity. Finally, from forall x: T_1(x) -> P(x), forall x: P(x) -> T_1(x) we can infer forall x: T_1(x) <-> P(x) via universal biconditional introduction. Therefore, the answer is yes.