Consider the following premises. James is not playing a game. For all y, y will climb a mountain if and only if y will play a game. Can we infer the following from them? If we can, name the inference rule being used: James is not climbing a mountain.
 From the fact that for all y, y will climb a mountain if and only if y will play a game we can infer that James is climbing a mountain if and only if James is playing a game via universal instantiation. Finally, from the fact that James is climbing a mountain if and only if James is playing a game, and that James is not playing a game we can infer that James is not climbing a mountain via biconditional elimination. Therefore, the answer is yes.