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