Consider the following premises. w -> r_13. p -> q. q -> s_3. s_3 -> w. r_13 -> s_3. Can we infer p -> r_13 from them? If possible, name the inference rules being used at each step.
 From s_3 -> w, w -> r_13 we can infer s_3 -> r_13 via transitivity. From p -> q, q -> s_3 we can infer p -> s_3 via transitivity. From s_3 -> r_13, r_13 -> s_3 we can infer s_3 <-> r_13 via biconditional introduction. From s_3 <-> r_13 we can infer s_3 -> r_13 via biconditional elimination. Finally, from p -> s_3, s_3 -> r_13 we can infer p -> r_13 via transitivity. Therefore, the answer is yes.