Consider the following premises. There is at least one x_15 for which if x_15 listens to a song, then x_15 is a poet. For all x_15, if x_15 drinks water, then x_15 is a police officer. For all x_15, x_15 is a poet if and only if x_15 will drink water. For all x_15, if x_15 were a police officer, then x_15 is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_15 for which if x_15 drinks water, then x_15 is a police officer.
 From the fact that for all x_15, x_15 is a poet if and only if x_15 will drink water we can infer that for all x_15, if x_15 were a poet, then x_15 is drinking water via universal biconditional elimination. From the fact that there is at least one x_15 for which if x_15 listens to a song, then x_15 is a poet, and that for all x_15, if x_15 were a poet, then x_15 is drinking water we can infer that there is at least one x_15 for which if x_15 listens to a song, then x_15 is drinking water via existential transitivity. From the fact that for all x_15, if x_15 were a police officer, then x_15 is listening to a song, and that there is at least one x_15 for which if x_15 listens to a song, then x_15 is drinking water we can infer that there is at least one x_15 for which if x_15 were a police officer, then x_15 is drinking water via existential transitivity. From the fact that there is at least one x_15 for which if x_15 were a police officer, then x_15 is drinking water, and that for all x_15, if x_15 drinks water, then x_15 is a police officer we can infer that there is at least one x_15 for which x_15 is a police officer if and only if x_15 will drink water via existential biconditional introduction. Finally, from the fact that there is at least one x_15 for which x_15 is a police officer if and only if x_15 will drink water we can infer that there is at least one x_15 for which if x_15 drinks water, then x_15 is a police officer via existential biconditional elimination. Therefore, the answer is yes.