Consider the following premises. For all y, y is a bartender if and only if y is sad. For all y, if y were sad, then y is a bartender. There is at least one y for which y is not a bartender. Can we infer the following from them? There is at least one y for which y is not sad.
 From the fact that for all y, y is a bartender if and only if y is sad we can infer that for all y, if y were a bartender, then y is sad. From the fact that for all y, if y were sad, then y is a bartender, and that for all y, if y were a bartender, then y is sad we can infer that for all y, y is sad if and only if y is a bartender. Finally, from the fact that for all y, y is sad if and only if y is a bartender, and that there is at least one y for which y is not a bartender we can infer that there is at least one y for which y is not sad. Therefore, the answer is yes.