Consider the following premises. For all x_5, if x_5 plays a game, then x_5 is climbing a mountain. For all x_5, if x_5 climbs a mountain, then x_5 is playing a game. There is at least one x_5 for which if x_5 were a janitor, then x_5 is climbing a mountain. Can we infer the following from them? There is at least one x_5 for which if x_5 were a janitor, then x_5 is playing a game.
 From the fact that for all x_5, if x_5 climbs a mountain, then x_5 is playing a game, and that for all x_5, if x_5 plays a game, then x_5 is climbing a mountain we can infer that for all x_5, x_5 will climb a mountain if and only if x_5 will play a game. From the fact that for all x_5, x_5 will climb a mountain if and only if x_5 will play a game we can infer that for all x_5, if x_5 climbs a mountain, then x_5 is playing a game. Finally, from the fact that there is at least one x_5 for which if x_5 were a janitor, then x_5 is climbing a mountain, and that for all x_5, if x_5 climbs a mountain, then x_5 is playing a game we can infer that there is at least one x_5 for which if x_5 were a janitor, then x_5 is playing a game. Therefore, the answer is yes.