Consider the following premises. For all z_1, z_1 is bored if and only if z_1 is sad. For all z_1, if z_1 were bored, then z_1 is an astronaut. There is at least one z_1 for which if z_1 were a police officer, then z_1 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_1 for which if z_1 were a police officer, then z_1 is an astronaut.
 From the fact that for all z_1, z_1 is bored if and only if z_1 is sad we can infer that for all z_1, if z_1 were sad, then z_1 is bored via universal biconditional elimination. From the fact that for all z_1, if z_1 were sad, then z_1 is bored, and that for all z_1, if z_1 were bored, then z_1 is an astronaut we can infer that for all z_1, if z_1 were sad, then z_1 is an astronaut via universal transitivity. Finally, from the fact that there is at least one z_1 for which if z_1 were a police officer, then z_1 is sad, and that for all z_1, if z_1 were sad, then z_1 is an astronaut we can infer that there is at least one z_1 for which if z_1 were a police officer, then z_1 is an astronaut via existential transitivity. Therefore, the answer is yes.