Consider the following premises. r_11 -> w. w -> r_1. t -> r_11. p_11 -> t. r_1 -> p_11. Can we infer p_11 <-> r_1 from them? If possible, name the inference rules being used at each step.
 From p_11 -> t, t -> r_11 we can infer p_11 -> r_11 via transitivity. From p_11 -> r_11, r_11 -> w we can infer p_11 -> w via transitivity. From p_11 -> w, w -> r_1 we can infer p_11 -> r_1 via transitivity. Finally, from p_11 -> r_1, r_1 -> p_11 we can infer p_11 <-> r_1 via biconditional introduction. Therefore, the answer is yes.