Consider the following premises. p -> r. r_2 <-> s. r -> s. Can we infer ~(p -> r_2) from them? If possible, name the inference rules being used at each step.
 From r_2 <-> s we can infer s -> r_2 via biconditional elimination. From r -> s, s -> r_2 we can infer r -> r_2 via transitivity. Finally, from p -> r, r -> r_2 we can infer p -> r_2 via transitivity, which contradicts ~(p -> r_2). Therefore, the answer is no.