Consider the following premises. T(j) -> w. w -> R_1(j). forall x: R_1(x) <-> T(x). Can we infer w <-> R_1(j) from them? If possible, name the inference rules being used at each step.
 From forall x: R_1(x) <-> T(x) we can infer R_1(j) <-> T(j) via universal instantiation. From R_1(j) <-> T(j) we can infer R_1(j) -> T(j) via biconditional elimination. From R_1(j) -> T(j), T(j) -> w we can infer R_1(j) -> w via transitivity. Finally, from w -> R_1(j), R_1(j) -> w we can infer w <-> R_1(j) via biconditional introduction. Therefore, the answer is yes.