Consider the following premises. For all y, y is a musician or y is not a bartender. For all y, if y were a musician, then y is a bartender. Can we infer the following from them? There is at least one y for which if is not true that y is a musician if and only if y is a bartender.
 From the fact that for all y, y is a musician or y is not a bartender we can infer that for all y, if y were a bartender, then y is a musician. Finally, from the fact that for all y, if y were a musician, then y is a bartender, and that for all y, if y were a bartender, then y is a musician we can infer that for all y, y is a musician if and only if y is a bartender, which contradicts that There is at least one y for which if is not true that y is a musician if and only if y is a bartender. Therefore, the answer is no.