Consider the following premises. Patricia is climbing a mountain if and only if James is playing a game. Patricia is climbing a mountain if and only if James is playing a game. Can we infer the following from them? If we can, name the inference rule being used: If is not true that James is playing a game if and only if Patricia is climbing a mountain.
 From the fact that Patricia is climbing a mountain if and only if James is playing a game we can infer that if James plays a game, then Patricia is climbing a mountain via biconditional elimination. From the fact that Patricia is climbing a mountain if and only if James is playing a game we can infer that if Patricia climbs a mountain, then James is playing a game via biconditional elimination. Finally, from the fact that if James plays a game, then Patricia is climbing a mountain, and that if Patricia climbs a mountain, then James is playing a game we can infer that James is playing a game if and only if Patricia is climbing a mountain via biconditional introduction, which contradicts that If is not true that James is playing a game if and only if Patricia is climbing a mountain. Therefore, the answer is no.