Consider the following premises. There is at least one x_9 for which x_9 is an office clerk if and only if x_9 will play a game. For all x_9, if x_9 were a nurse, then x_9 is playing a game. For all x_9, if x_9 climbs a mountain, then x_9 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which if x_9 climbs a mountain, then x_9 is an office clerk.
 From the fact that there is at least one x_9 for which x_9 is an office clerk if and only if x_9 will play a game we can infer that there is at least one x_9 for which if x_9 plays a game, then x_9 is an office clerk via existential biconditional elimination. From the fact that for all x_9, if x_9 climbs a mountain, then x_9 is a nurse, and that for all x_9, if x_9 were a nurse, then x_9 is playing a game we can infer that for all x_9, if x_9 climbs a mountain, then x_9 is playing a game via universal transitivity. Finally, from the fact that for all x_9, if x_9 climbs a mountain, then x_9 is playing a game, and that there is at least one x_9 for which if x_9 plays a game, then x_9 is an office clerk we can infer that there is at least one x_9 for which if x_9 climbs a mountain, then x_9 is an office clerk via existential transitivity. Therefore, the answer is yes.