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