Consider the following premises. For all x_12, x_12 will write a letter if and only if x_12 is a writer. There is at least one x_12 for which if x_12 were a writer, then x_12 is making tea. For all x_12, x_12 will make tea if and only if x_12 will write a letter. Can we infer the following from them? There is at least one x_12 for which if x_12 were a writer, then x_12 is making tea.
That is one of the premises. Therefore, the answer is yes.