Consider the following premises. Richard is playing a game if and only if it is raining. If Richard plays a game, then James is not a police officer. For all y, y is a police officer. 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 y, y is a police officer we can infer that James is a police officer via universal instantiation. From the fact that if Richard plays a game, then James is not a police officer, and that James is a police officer we can infer that Richard is not playing a game via modus tollens. Finally, from the fact that Richard is playing a game if and only if it is raining, and that Richard is not playing a game we can infer that it is not raining via biconditional elimination. Therefore, the answer is yes.