Consider the following premises. For all x_6, if x_6 plays a game, then x_6 is climbing a mountain. For all x_6, if x_6 climbs a mountain, then x_6 is happy. For all x_6, if x_6 were curious, then x_6 is happy. For all x_6, if x_6 were happy, then x_6 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, if x_6 were curious, then x_6 is playing a game.
 From the fact that for all x_6, if x_6 plays a game, then x_6 is climbing a mountain, and that for all x_6, if x_6 climbs a mountain, then x_6 is happy we can infer that for all x_6, if x_6 plays a game, then x_6 is happy via universal transitivity. From the fact that for all x_6, if x_6 plays a game, then x_6 is happy, and that for all x_6, if x_6 were happy, then x_6 is playing a game we can infer that for all x_6, x_6 will play a game if and only if x_6 is happy via universal biconditional introduction. From the fact that for all x_6, x_6 will play a game if and only if x_6 is happy we can infer that for all x_6, if x_6 were happy, then x_6 is playing a game via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 were curious, then x_6 is happy, and that for all x_6, if x_6 were happy, then x_6 is playing a game we can infer that for all x_6, if x_6 were curious, then x_6 is playing a game via universal transitivity. Therefore, the answer is yes.