Consider the following premises. For all y, if y climbs a mountain, then y is excited. For all y, if y were excited, then y is writing a letter. For all y, y will climb a mountain or y will not write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all y, if y climbs a mountain, then y is writing a letter.
We can infer this via the universal transitivity rule. Therefore, the answer is yes.