Consider the following premises. For all x_15, if x_15 climbs a mountain, then x_15 is a cashier. Jessica is not bored. Robert is a writer if and only if Jennifer is climbing a mountain. Jennifer is a cashier if and only if Jessica is bored. Can we infer the following from them? If we can, name the inference rule being used: Robert is not a writer.
 From the fact that for all x_15, if x_15 climbs a mountain, then x_15 is a cashier we can infer that if Jennifer climbs a mountain, then Jennifer is a cashier via universal instantiation. From the fact that Jennifer is a cashier if and only if Jessica is bored, and that Jessica is not bored we can infer that Jennifer is not a cashier via biconditional elimination. From the fact that if Jennifer climbs a mountain, then Jennifer is a cashier, and that Jennifer is not a cashier we can infer that Jennifer is not climbing a mountain via modus tollens. Finally, from the fact that Robert is a writer if and only if Jennifer is climbing a mountain, and that Jennifer is not climbing a mountain we can infer that Robert is not a writer via biconditional elimination. Therefore, the answer is yes.