Consider the following premises. For all x_10, if x_10 were excited, then x_10 is climbing a mountain. If it is late, then David is not climbing a mountain. For all x_10, x_10 is excited. Can we infer the following from them? If we can, name the inference rule being used: If it is late, then David is not climbing a mountain.
That is one of the premises. Therefore, the answer is yes.