Consider the following premises. For all y, y is a nurse if and only if y will drink water. There is at least one y for which y is not a nurse. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y will not drink water.
 From the fact that for all y, y is a nurse if and only if y will drink water we can infer that for all y, if y drinks water, then y is a nurse via universal biconditional elimination. Finally, from the fact that for all y, if y drinks water, then y is a nurse, and that there is at least one y for which y is not a nurse we can infer that there is at least one y for which y will not drink water via existential modus tollens. Therefore, the answer is yes.