Consider the following premises. r <-> w. w -> r_2. ~r. r_2 -> w. Can we infer ~r_2 from them? If possible, name the inference rules being used at each step.
 From r <-> w, ~r we can infer ~w via biconditional elimination. From w -> r_2, r_2 -> w we can infer w <-> r_2 via biconditional introduction. Finally, from w <-> r_2, ~w we can infer ~r_2 via biconditional elimination. Therefore, the answer is yes.