Consider the following premises. There is at least one y for which if y were a nurse, then y is poor. For all y, if y were poor, then y is a janitor. For all y, if y were a janitor, then y is a nurse. Can we infer the following from them? For all y, the fact that y were poor does not imply that y is a nurse.
That contradicts the premises. Therefore the answer is no.