Consider the following premises. w -> r. r -> r_3. ~w. r_3 -> w. Can we infer ~r_3 from them? If possible, name the inference rules being used at each step.
 From w -> r, r -> r_3 we can infer w -> r_3 via transitivity. From w -> r_3, r_3 -> w we can infer w <-> r_3 via biconditional introduction. Finally, from w <-> r_3, ~w we can infer ~r_3 via biconditional elimination. Therefore, the answer is yes.