Consider the following premises. w -> r_8. r_8 -> u_1. p_8 -> w. u_1 -> r_8. Can we infer p_8 -> u_1 from them? If possible, name the inference rules being used at each step.
 From p_8 -> w, w -> r_8 we can infer p_8 -> r_8 via transitivity. From r_8 -> u_1, u_1 -> r_8 we can infer r_8 <-> u_1 via biconditional introduction. From r_8 <-> u_1 we can infer r_8 -> u_1 via biconditional elimination. Finally, from p_8 -> r_8, r_8 -> u_1 we can infer p_8 -> u_1 via transitivity. Therefore, the answer is yes.