Consider the following premises. r_8 -> p_3. r -> r_8. p_3 -> r_8. p_3 -> r. Can we infer ~(p_3 <-> r_8) from them? If possible, name the inference rules being used at each step.
 From p_3 -> r, r -> r_8 we can infer p_3 -> r_8 via transitivity. From r_8 -> p_3, p_3 -> r_8 we can infer r_8 <-> p_3 via biconditional introduction. From r_8 <-> p_3 we can infer r_8 -> p_3 via biconditional elimination. Finally, from p_3 -> r_8, r_8 -> p_3 we can infer p_3 <-> r_8 via biconditional introduction, which contradicts ~(p_3 <-> r_8). Therefore, the answer is no.