Consider the following premises. For all y, y is a soldier. Susan is playing tennis if and only if it is raining. For all y, y will play tennis if and only if y will drink water. For all y, if y drinks water, then y is not a soldier. 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, if y drinks water, then y is not a soldier, and that for all y, y is a soldier we can infer that for all y, y will not drink water via universal modus tollens. From the fact that for all y, y will play tennis if and only if y will drink water, and that for all y, y will not drink water we can infer that for all y, y will not play tennis via universal biconditional elimination. From the fact that for all y, y will not play tennis we can infer that Susan is not playing tennis via universal instantiation. Finally, from the fact that Susan is playing tennis if and only if it is raining, and that Susan is not playing tennis we can infer that it is not raining via biconditional elimination. Therefore, the answer is yes.