Consider the following premises. For all x_3, if x_3 were an electrician, then x_3 is taking a plane. For all x_3, x_3 is an electrician. For all x_3, if x_3 takes a plane, then x_3 is climbing a mountain. There is at least one x_3 for which if x_3 sleeps, then x_3 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_3 for which x_3 will climb a mountain.
 From the fact that for all x_3, if x_3 were an electrician, then x_3 is taking a plane, and that for all x_3, if x_3 takes a plane, then x_3 is climbing a mountain we can infer that for all x_3, if x_3 were an electrician, then x_3 is climbing a mountain via universal transitivity. From the fact that for all x_3, x_3 is an electrician we can infer that for all x_3, x_3 is an electrician or x_3 will sleep via universal addition. Finally, from the fact that for all x_3, if x_3 were an electrician, then x_3 is climbing a mountain, that there is at least one x_3 for which if x_3 sleeps, then x_3 is climbing a mountain, and that for all x_3, x_3 is an electrician or x_3 will sleep we can infer that there is at least one x_3 for which x_3 will climb a mountain via existential disjunction elimination. Therefore, the answer is yes.