Consider the following premises. There is at least one x_1 for which if x_1 climbs a mountain, then x_1 is making tea. For all x_1, x_1 will make tea and x_1 will write a letter. For all x_1, if x_1 makes tea, then x_1 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_1 for which if x_1 climbs a mountain, then x_1 is making tea.
That is one of the premises. Therefore, the answer is yes.