Consider the following premises. For all y, y is a lawyer if and only if y is a bartender. For all y, if y were a bartender, then y is fast. There is at least one y for which if y were fast, then y is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: For all y, y is a lawyer if and only if y is a bartender.
That is one of the premises. Therefore, the answer is yes.