Consider the following premises. There is at least one y for which if y were a lawyer, then y is a police officer. For all y, if y were a police officer, then y is a lawyer. For all y, y is a lawyer if and only if y is a doctor. For all y, y is not a police officer. Can we infer the following from them? There is at least one y for which y is not a doctor.
 From the fact that for all y, if y were a police officer, then y is a lawyer, and that there is at least one y for which if y were a lawyer, then y is a police officer we can infer that there is at least one y for which y is a police officer if and only if y is a lawyer. From the fact that there is at least one y for which y is a police officer if and only if y is a lawyer, and that for all y, y is not a police officer we can infer that there is at least one y for which y is not a lawyer. Finally, from the fact that for all y, y is a lawyer if and only if y is a doctor, and that there is at least one y for which y is not a lawyer we can infer that there is at least one y for which y is not a doctor. Therefore, the answer is yes.