Consider the following premises. There is at least one x_4 for which if x_4 works, then x_4 is climbing a mountain. For all x_4, if x_4 were an astronaut, then x_4 is climbing a mountain. For all x_4, if x_4 drinks water, then x_4 is working. For all x_4, x_4 is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 will climb a mountain.
 From the fact that for all x_4, if x_4 drinks water, then x_4 is working, and that there is at least one x_4 for which if x_4 works, then x_4 is climbing a mountain we can infer that there is at least one x_4 for which if x_4 drinks water, then x_4 is climbing a mountain via existential transitivity. From the fact that for all x_4, x_4 is an astronaut we can infer that for all x_4, x_4 is an astronaut or x_4 will drink water via universal addition. Finally, from the fact that for all x_4, if x_4 were an astronaut, then x_4 is climbing a mountain, that there is at least one x_4 for which if x_4 drinks water, then x_4 is climbing a mountain, and that for all x_4, x_4 is an astronaut or x_4 will drink water we can infer that there is at least one x_4 for which x_4 will climb a mountain via existential disjunction elimination. Therefore, the answer is yes.