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