Consider the following premises. For all x_4, if x_4 were a doctor, then x_4 is a writer. For all x_4, x_4 is excited or x_4 is a doctor. For all x_4, if x_4 were a police officer, then x_4 is a writer. For all x_4, x_4 is not excited. Can we infer the following from them? For all x_4, x_4 is a writer.
 From the fact that for all x_4, x_4 is excited or x_4 is a doctor, and that for all x_4, x_4 is not excited we can infer that for all x_4, x_4 is a doctor. From the fact that for all x_4, x_4 is a doctor we can infer that for all x_4, x_4 is a doctor or x_4 is a police officer. Finally, from the fact that for all x_4, if x_4 were a doctor, then x_4 is a writer, that for all x_4, if x_4 were a police officer, then x_4 is a writer, and that for all x_4, x_4 is a doctor or x_4 is a police officer we can infer that for all x_4, x_4 is a writer. Therefore, the answer is yes.