Consider the following premises. For all z, if z drinks water, then z is working. For all z, if z works, then z is drinking water. There is at least one z for which if z works, then z is drinking water. 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 will work if and only if z will drink water.
 From the fact that for all z, if z drinks water, then z is working, and that there is at least one z for which if z works, then z is drinking water we can infer that there is at least one z for which z will drink water if and only if z will work via existential biconditional introduction. From the fact that there is at least one z for which z will drink water if and only if z will work we can infer that there is at least one z for which if z drinks water, then z is working via existential biconditional elimination. Finally, from the fact that for all z, if z works, then z is drinking water, and that there is at least one z for which if z drinks water, then z is working we can infer that there is at least one z for which z will work if and only if z will drink water via existential biconditional introduction, which contradicts that For all z, if is not true that z will work if and only if z will drink water. Therefore, the answer is no.