Consider the following premises. For all y, if y were a scientist, then y is drinking water. For all y, y is not a lawyer. There is at least one y for which if y drinks water, then y is a lawyer. 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 is not a scientist.
 From the fact that for all y, if y were a scientist, then y is drinking water, and that there is at least one y for which if y drinks water, then y is a lawyer we can infer that there is at least one y for which if y were a scientist, then y is a lawyer via existential transitivity. Finally, from the fact that there is at least one y for which if y were a scientist, then y is a lawyer, and that for all y, y is not a lawyer we can infer that there is at least one y for which y is not a scientist via existential modus tollens. Therefore, the answer is yes.