Consider the following premises. Elisabeth is an office clerk or John is a police officer. For all z, if z were a police officer, then z is a bartender. If Elisabeth were an office clerk, then John is a bartender. For all z, if z were a bartender, then z is a police officer. Can we infer the following from them? John is a bartender.
 From the fact that for all z, if z were a bartender, then z is a police officer, and that for all z, if z were a police officer, then z is a bartender we can infer that for all z, z is a bartender if and only if z is a police officer. From the fact that for all z, z is a bartender if and only if z is a police officer we can infer that John is a bartender if and only if John is a police officer. From the fact that John is a bartender if and only if John is a police officer we can infer that if John were a police officer, then John is a bartender. Finally, from the fact that if Elisabeth were an office clerk, then John is a bartender, that if John were a police officer, then John is a bartender, and that Elisabeth is an office clerk or John is a police officer we can infer that John is a bartender. Therefore, the answer is yes.