Consider the following premises. William is playing a game or it is not cold. It is not cold. It is cold if and only if William is playing a game. If Elisabeth plays squash, then William is playing a game. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not playing squash.
 From the fact that William is playing a game or it is not cold we can infer that if it is cold, then William is playing a game via rewriting. From the fact that it is cold if and only if William is playing a game we can infer that if William plays a game, then it is cold via biconditional elimination. From the fact that if it is cold, then William is playing a game, and that if William plays a game, then it is cold we can infer that it is cold if and only if William is playing a game via biconditional introduction. From the fact that it is cold if and only if William is playing a game, and that it is not cold we can infer that William is not playing a game via biconditional elimination. Finally, from the fact that if Elisabeth plays squash, then William is playing a game, and that William is not playing a game we can infer that Elisabeth is not playing squash via modus tollens. Therefore, the answer is yes.