Consider the following premises. Richard is making tea if and only if Richard is a doctor. For all y, y will make tea if and only if y is a doctor. Can we infer the following from them? Richard is a doctor if and only if Richard is making tea.
 From the fact that for all y, y will make tea if and only if y is a doctor we can infer that Richard is making tea if and only if Richard is a doctor. From the fact that Richard is making tea if and only if Richard is a doctor we can infer that if Richard makes tea, then Richard is a doctor. From the fact that Richard is making tea if and only if Richard is a doctor we can infer that if Richard were a doctor, then Richard is making tea. Finally, from the fact that if Richard were a doctor, then Richard is making tea, and that if Richard makes tea, then Richard is a doctor we can infer that Richard is a doctor if and only if Richard is making tea. Therefore, the answer is yes.