Consider the following premises. For all x_7, if x_7 were a scientist, then x_7 is climbing a mountain. There is at least one x_7 for which if x_7 reads a book, then x_7 is climbing a mountain. For all x_7, x_7 will read a book or x_7 is a scientist. For all x_7, x_7 is a musician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will climb a mountain and x_7 is a musician.
 From the fact that there is at least one x_7 for which if x_7 reads a book, then x_7 is climbing a mountain, that for all x_7, if x_7 were a scientist, then x_7 is climbing a mountain, and that for all x_7, x_7 will read a book or x_7 is a scientist we can infer that there is at least one x_7 for which x_7 will climb a mountain via existential disjunction elimination. Finally, from the fact that there is at least one x_7 for which x_7 will climb a mountain, and that for all x_7, x_7 is a musician we can infer that there is at least one x_7 for which x_7 will climb a mountain and x_7 is a musician via existential conjunction. Therefore, the answer is yes.