Consider the following premises. There is at least one x for which if x reads a book, then x is a doctor. For all x, if x were a doctor, then x is a police officer. For all x, x will read a book if and only if x is a police officer. Can we infer the following from them? There is at least one x for which x will read a book if and only if x is a police officer.
 From the fact that there is at least one x for which if x reads a book, then x is a doctor, and that for all x, if x were a doctor, then x is a police officer we can infer that there is at least one x for which if x reads a book, then x is a police officer. From the fact that for all x, x will read a book if and only if x is a police officer we can infer that for all x, if x were a police officer, then x is reading a book. Finally, from the fact that there is at least one x for which if x reads a book, then x is a police officer, and that for all x, if x were a police officer, then x is reading a book we can infer that there is at least one x for which x will read a book if and only if x is a police officer. Therefore, the answer is yes.