Consider the following premises. For all z, z is a musician if and only if z is a bartender. There is at least one z for which if z were a poet, then z is a musician. For all z, if z were a bartender, then z is a poet. Can we infer the following from them? If we can, name the inference rule being used: For all z, if is not true that z is a bartender if and only if z is a poet.
That contradicts the premises. Therefore the answer is no.