Consider the following premises. For all y, y is not a nurse. William is a poet if and only if it is sunny. If William were a poet, then Robert is a nurse. Can we infer the following from them? It is not sunny.
 From the fact that for all y, y is not a nurse we can infer that Robert is not a nurse. From the fact that if William were a poet, then Robert is a nurse, and that Robert is not a nurse we can infer that William is not a poet. Finally, from the fact that William is a poet if and only if it is sunny, and that William is not a poet we can infer that it is not sunny. Therefore, the answer is yes.