Consider the following premises. For all x_5, x_5 is a scientist if and only if x_5 is a writer. For all x_5, if x_5 sleeps, then x_5 is a scientist. For all x_5, if x_5 were sad, then x_5 is sleeping. Can we infer the following from them? For all x_5, if x_5 were sad, then x_5 is a writer.
 From the fact that for all x_5, if x_5 were sad, then x_5 is sleeping, and that for all x_5, if x_5 sleeps, then x_5 is a scientist we can infer that for all x_5, if x_5 were sad, then x_5 is a scientist. From the fact that for all x_5, x_5 is a scientist if and only if x_5 is a writer we can infer that for all x_5, if x_5 were a scientist, then x_5 is a writer. Finally, from the fact that for all x_5, if x_5 were sad, then x_5 is a scientist, and that for all x_5, if x_5 were a scientist, then x_5 is a writer we can infer that for all x_5, if x_5 were sad, then x_5 is a writer. Therefore, the answer is yes.