Consider the following premises. forall y: T(y) -> U_2(y). forall y: U_2(y) -> T(y). ~U_2(h). Can we infer T(h) from them? If possible, name the inference rules being used at each step.
 From forall y: U_2(y) -> T(y), forall y: T(y) -> U_2(y) we can infer forall y: U_2(y) <-> T(y) via universal biconditional introduction. From forall y: U_2(y) <-> T(y) we can infer U_2(h) <-> T(h) via universal instantiation. Finally, from U_2(h) <-> T(h), ~U_2(h) we can infer ~T(h) via biconditional elimination, which contradicts T(h). Therefore, the answer is no.