Consider the following premises. For all z, if z plays tennis, then z is making tea. For all z, z will not play tennis. For all z, z will make tea if and only if z will play tennis. Can we infer the following from them? For all z, z will not make tea.
 From the fact that for all z, z will make tea if and only if z will play tennis we can infer that for all z, if z makes tea, then z is playing tennis. From the fact that for all z, if z makes tea, then z is playing tennis, and that for all z, if z plays tennis, then z is making tea we can infer that for all z, z will make tea if and only if z will play tennis. Finally, from the fact that for all z, z will make tea if and only if z will play tennis, and that for all z, z will not play tennis we can infer that for all z, z will not make tea. Therefore, the answer is yes.