Consider the following premises. For all y_2, if y_2 were a police officer, then y_2 is sleeping. For all y_2, if y_2 were happy, then y_2 is sleeping. There is at least one y_2 for which if y_2 sleeps, then y_2 is happy. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_2 for which if y_2 were a police officer, then y_2 is happy.
 From the fact that there is at least one y_2 for which if y_2 sleeps, then y_2 is happy, and that for all y_2, if y_2 were happy, then y_2 is sleeping we can infer that there is at least one y_2 for which y_2 will sleep if and only if y_2 is happy via existential biconditional introduction. From the fact that there is at least one y_2 for which y_2 will sleep if and only if y_2 is happy we can infer that there is at least one y_2 for which if y_2 sleeps, then y_2 is happy via existential biconditional elimination. Finally, from the fact that for all y_2, if y_2 were a police officer, then y_2 is sleeping, and that there is at least one y_2 for which if y_2 sleeps, then y_2 is happy we can infer that there is at least one y_2 for which if y_2 were a police officer, then y_2 is happy via existential transitivity. Therefore, the answer is yes.