Consider the following premises. p_1 -> r. ~p_1. r -> p_1. Can we infer ~r from them? If possible, name the inference rules being used at each step.
 From p_1 -> r, r -> p_1 we can infer p_1 <-> r via biconditional introduction. Finally, from p_1 <-> r, ~p_1 we can infer ~r via biconditional elimination. Therefore, the answer is yes.