Consider the following premises. There is at least one x for which if x were a police officer, then x is a janitor. For all x, x is not a police officer. For all x, x is a police officer or x is not a janitor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x is not a janitor.
 From the fact that for all x, x is a police officer or x is not a janitor we can infer that for all x, if x were a janitor, then x is a police officer via universal rewriting. From the fact that for all x, if x were a janitor, then x is a police officer, and that there is at least one x for which if x were a police officer, then x is a janitor we can infer that there is at least one x for which x is a janitor if and only if x is a police officer via existential biconditional introduction. Finally, from the fact that there is at least one x for which x is a janitor if and only if x is a police officer, and that for all x, x is not a police officer we can infer that there is at least one x for which x is not a janitor via existential biconditional elimination. Therefore, the answer is yes.