Consider the following premises. For all x_13, x_13 is sad if and only if x_13 is a writer. Mary is a cashier. If Mary were a cashier, then James is sad. Can we infer the following from them? If we can, name the inference rule being used: James is not a writer.
 From the fact that for all x_13, x_13 is sad if and only if x_13 is a writer we can infer that for all x_13, if x_13 were sad, then x_13 is a writer via universal biconditional elimination. From the fact that for all x_13, if x_13 were sad, then x_13 is a writer we can infer that if James were sad, then James is a writer via universal instantiation. From the fact that if Mary were a cashier, then James is sad, and that if James were sad, then James is a writer we can infer that if Mary were a cashier, then James is a writer via transitivity. Finally, from the fact that if Mary were a cashier, then James is a writer, and that Mary is a cashier we can infer that James is a writer via modus ponens, which contradicts that James is not a writer. Therefore, the answer is no.