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