Consider the following premises. There is at least one x for which if x were a police officer, then x is making tea. For all x, if x writes a letter, then x is making tea. For all x, if x makes tea, then x is a police officer. Can we infer the following from them? There is at least one x for which if x writes a letter, then x is a police officer.
 From the fact that for all x, if x makes tea, 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 making tea we can infer that there is at least one x for which x will make tea if and only if x is a police officer. From the fact that there is at least one x for which x will make tea if and only if x is a police officer we can infer that there is at least one x for which if x makes tea, then x is a police officer. Finally, from the fact that for all x, if x writes a letter, then x is making tea, and that there is at least one x for which if x makes tea, then x is a police officer we can infer that there is at least one x for which if x writes a letter, then x is a police officer. Therefore, the answer is yes.