Consider the following premises. For all z_2, z_2 will climb a mountain if and only if z_2 will work. For all z_2, if z_2 listens to a song, then z_2 is driving a car. For all z_2, z_2 will sleep if and only if z_2 will listen to a song. There is at least one z_2 for which if z_2 drives a car, then z_2 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 z_2 for which if z_2 sleeps, then z_2 is working.
 From the fact that for all z_2, z_2 will sleep if and only if z_2 will listen to a song we can infer that for all z_2, if z_2 sleeps, then z_2 is listening to a song via universal biconditional elimination. From the fact that for all z_2, if z_2 sleeps, then z_2 is listening to a song, and that for all z_2, if z_2 listens to a song, then z_2 is driving a car we can infer that for all z_2, if z_2 sleeps, then z_2 is driving a car via universal transitivity. From the fact that for all z_2, z_2 will climb a mountain if and only if z_2 will work we can infer that for all z_2, if z_2 climbs a mountain, then z_2 is working via universal biconditional elimination. From the fact that there is at least one z_2 for which if z_2 drives a car, then z_2 is climbing a mountain, and that for all z_2, if z_2 climbs a mountain, then z_2 is working we can infer that there is at least one z_2 for which if z_2 drives a car, then z_2 is working via existential transitivity. Finally, from the fact that for all z_2, if z_2 sleeps, then z_2 is driving a car, and that there is at least one z_2 for which if z_2 drives a car, then z_2 is working we can infer that there is at least one z_2 for which if z_2 sleeps, then z_2 is working via existential transitivity. Therefore, the answer is yes.