Consider the following premises. There is at least one x_14 for which if x_14 reads a book, then x_14 is writing a letter. For all x_14, x_14 is a writer if and only if x_14 will read a book. For all x_14, x_14 will write a letter if and only if x_14 will read a book. Can we infer the following from them? There is at least one x_14 for which if x_14 writes a letter, then x_14 is a writer.
 From the fact that for all x_14, x_14 will write a letter if and only if x_14 will read a book we can infer that for all x_14, if x_14 writes a letter, then x_14 is reading a book. From the fact that for all x_14, x_14 is a writer if and only if x_14 will read a book we can infer that for all x_14, if x_14 reads a book, then x_14 is a writer. From the fact that there is at least one x_14 for which if x_14 reads a book, then x_14 is writing a letter, and that for all x_14, if x_14 writes a letter, then x_14 is reading a book we can infer that there is at least one x_14 for which x_14 will read a book if and only if x_14 will write a letter. From the fact that there is at least one x_14 for which x_14 will read a book if and only if x_14 will write a letter we can infer that there is at least one x_14 for which if x_14 writes a letter, then x_14 is reading a book. Finally, from the fact that there is at least one x_14 for which if x_14 writes a letter, then x_14 is reading a book, and that for all x_14, if x_14 reads a book, then x_14 is a writer we can infer that there is at least one x_14 for which if x_14 writes a letter, then x_14 is a writer. Therefore, the answer is yes.