Consider the following premises. For all y_4, if y_4 writes a letter, then y_4 is a janitor. For all y_4, if y_4 were a police officer, then y_4 is not a janitor. There is at least one y_4 for which if y_4 were a scientist, then y_4 is a janitor. For all y_4, y_4 is a scientist or y_4 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_4 for which y_4 is not a police officer.
 From the fact that there is at least one y_4 for which if y_4 were a scientist, then y_4 is a janitor, that for all y_4, if y_4 writes a letter, then y_4 is a janitor, and that for all y_4, y_4 is a scientist or y_4 will write a letter we can infer that there is at least one y_4 for which y_4 is a janitor via existential disjunction elimination. Finally, from the fact that for all y_4, if y_4 were a police officer, then y_4 is not a janitor, and that there is at least one y_4 for which y_4 is a janitor we can infer that there is at least one y_4 for which y_4 is not a police officer via existential modus tollens. Therefore, the answer is yes.