Consider the following premises. U_1(j) -> t. forall z: T_2(z) <-> U_1(z). t -> U_1(j). ~t. Can we infer ~T_2(j) from them? If possible, name the inference rules being used at each step.
 From forall z: T_2(z) <-> U_1(z) we can infer T_2(j) <-> U_1(j) via universal instantiation. From t -> U_1(j), U_1(j) -> t we can infer t <-> U_1(j) via biconditional introduction. From t <-> U_1(j), ~t we can infer ~U_1(j) via biconditional elimination. Finally, from T_2(j) <-> U_1(j), ~U_1(j) we can infer ~T_2(j) via biconditional elimination. Therefore, the answer is yes.