Consider the following premises. For all z, z will play a game or z is not a writer. There is at least one z for which z is a bartender if and only if z will play a game. Can we infer the following from them? If we can, name the inference rule being used: For all z, the fact that z were a writer does not imply that z is a bartender.
 From the fact that there is at least one z for which z is a bartender if and only if z will play a game we can infer that there is at least one z for which if z plays a game, then z is a bartender via existential biconditional elimination. Finally, from the fact that for all z, z will play a game or z is not a writer we can infer that for all z, if z were a writer, then z is playing a game via universal rewriting, which contradicts that For all z, the fact that z were a writer does not imply that z is a bartender. Therefore, the answer is no.