Consider the following premises. For all x_6, if x_6 were poor, then x_6 is playing a game. For all x_6, x_6 will climb a mountain or x_6 will not make tea. For all x_6, if x_6 plays a game, then x_6 is making tea. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, if x_6 were poor, then x_6 is climbing a mountain.
 From the fact that for all x_6, x_6 will climb a mountain or x_6 will not make tea we can infer that for all x_6, if x_6 makes tea, then x_6 is climbing a mountain via universal rewriting. From the fact that for all x_6, if x_6 plays a game, then x_6 is making tea, and that for all x_6, if x_6 makes tea, then x_6 is climbing a mountain we can infer that for all x_6, if x_6 plays a game, then x_6 is climbing a mountain via universal transitivity. Finally, from the fact that for all x_6, if x_6 were poor, then x_6 is playing a game, and that for all x_6, if x_6 plays a game, then x_6 is climbing a mountain we can infer that for all x_6, if x_6 were poor, then x_6 is climbing a mountain via universal transitivity. Therefore, the answer is yes.