Consider the following premises. For all x_7, if x_7 writes a letter, then x_7 is rich. For all x_7, if x_7 were rich, then x_7 is writing a letter. For all x_7, if x_7 were rich, then x_7 is reading a book. For all x_7, x_7 will not write a letter. There is at least one x_7 for which if x_7 reads a book, then x_7 is rich. Can we infer the following from them? For all x_7, if x_7 were rich, then x_7 is reading a book.
That is one of the premises. Therefore, the answer is yes.