Consider the following premises. For all x, if x drinks water, then x is poor. For all x, x is not poor. For all x, if x drinks water, then x is a nurse. There is at least one x for which if x were a nurse, then x is drinking water. Can we infer the following from them? If we can, name the inference rule being used: For all x, x is a nurse.
 From the fact that there is at least one x for which if x were a nurse, then x is drinking water, and that for all x, if x drinks water, then x is a nurse we can infer that there is at least one x for which x is a nurse if and only if x will drink water via existential biconditional introduction. From the fact that for all x, if x drinks water, then x is poor, and that for all x, x is not poor we can infer that for all x, x will not drink water via universal modus tollens. Finally, from the fact that there is at least one x for which x is a nurse if and only if x will drink water, and that for all x, x will not drink water we can infer that there is at least one x for which x is not a nurse via existential biconditional elimination, which contradicts that For all x, x is a nurse. Therefore, the answer is no.