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