Consider the following premises. If Richard were an astronaut, then Jessica is a writer. If Mary were a cashier, then Barbara is cooking. If Barbara cooks, then Richard is an astronaut. If Jessica were a writer, then Mary is a cashier. Jessica is not a writer. Can we infer the following from them? If we can, name the inference rule being used: Mary is not a cashier.
 From the fact that if Barbara cooks, then Richard is an astronaut, and that if Richard were an astronaut, then Jessica is a writer we can infer that if Barbara cooks, then Jessica is a writer via transitivity. From the fact that if Mary were a cashier, then Barbara is cooking, and that if Barbara cooks, then Jessica is a writer we can infer that if Mary were a cashier, then Jessica is a writer via transitivity. From the fact that if Mary were a cashier, then Jessica is a writer, and that if Jessica were a writer, then Mary is a cashier we can infer that Mary is a cashier if and only if Jessica is a writer via biconditional introduction. Finally, from the fact that Mary is a cashier if and only if Jessica is a writer, and that Jessica is not a writer we can infer that Mary is not a cashier via biconditional elimination. Therefore, the answer is yes.