Consider the following premises. For all x_9, x_9 is not fast. If it rains, then William is a writer. For all x_9, x_9 is a writer if and only if x_9 is fast. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that for all x_9, x_9 is a writer if and only if x_9 is fast, and that for all x_9, x_9 is not fast we can infer that for all x_9, x_9 is not a writer via universal biconditional elimination. From the fact that for all x_9, x_9 is not a writer we can infer that William is not a writer via universal instantiation. Finally, from the fact that if it rains, then William is a writer, and that William is not a writer we can infer that it is not raining via modus tollens. Therefore, the answer is yes.