Consider the following premises. If William drinks water, then Elisabeth is playing a game. If Elisabeth plays a game, then William is drinking water. William is not drinking water. If William drinks water, then Elisabeth is playing a game. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not playing a game.
 From the fact that if William drinks water, then Elisabeth is playing a game, and that if Elisabeth plays a game, then William is drinking water we can infer that William is drinking water if and only if Elisabeth is playing a game via biconditional introduction. From the fact that William is drinking water if and only if Elisabeth is playing a game we can infer that if Elisabeth plays a game, then William is drinking water via biconditional elimination. From the fact that if William drinks water, then Elisabeth is playing a game, and that if Elisabeth plays a game, then William is drinking water we can infer that William is drinking water if and only if Elisabeth is playing a game via biconditional introduction. Finally, from the fact that William is drinking water if and only if Elisabeth is playing a game, and that William is not drinking water we can infer that Elisabeth is not playing a game via biconditional elimination. Therefore, the answer is yes.