Consider the following premises. ~r. p -> u_2. r <-> p. r or ~u_2. Can we infer u_2 from them? If possible, name the inference rules being used at each step.
 From r <-> p we can infer r -> p via biconditional elimination. From r -> p, p -> u_2 we can infer r -> u_2 via transitivity. From r or ~u_2 we can infer u_2 -> r via rewriting. From u_2 -> r, r -> u_2 we can infer u_2 <-> r via biconditional introduction. Finally, from u_2 <-> r, ~r we can infer ~u_2 via biconditional elimination, which contradicts u_2. Therefore, the answer is no.