Consider the following premises. For all z, z will cook if and only if z is a doctor. For all z, z will cook if and only if z is a doctor. Can we infer the following from them? There is at least one z for which if is not true that z is a doctor if and only if z will cook.
 From the fact that for all z, z will cook if and only if z is a doctor we can infer that for all z, if z cooks, then z is a doctor. From the fact that for all z, z will cook if and only if z is a doctor we can infer that for all z, if z were a doctor, then z is cooking. Finally, from the fact that for all z, if z were a doctor, then z is cooking, and that for all z, if z cooks, then z is a doctor we can infer that for all z, z is a doctor if and only if z will cook, which contradicts that There is at least one z for which if is not true that z is a doctor if and only if z will cook. Therefore, the answer is no.