Consider the following premises. For all z_4, if z_4 were poor, then z_4 is making tea. There is at least one z_4 for which if z_4 were poor, then z_4 is making tea. For all z_4, if z_4 makes tea, then z_4 is poor. Can we infer the following from them? There is at least one z_4 for which z_4 is poor if and only if z_4 will make tea.
 From the fact that for all z_4, if z_4 makes tea, then z_4 is poor, and that for all z_4, if z_4 were poor, then z_4 is making tea we can infer that for all z_4, z_4 will make tea if and only if z_4 is poor. From the fact that for all z_4, z_4 will make tea if and only if z_4 is poor we can infer that for all z_4, if z_4 makes tea, then z_4 is poor. Finally, from the fact that there is at least one z_4 for which if z_4 were poor, then z_4 is making tea, and that for all z_4, if z_4 makes tea, then z_4 is poor we can infer that there is at least one z_4 for which z_4 is poor if and only if z_4 will make tea. Therefore, the answer is yes.