Consider the following premises. For all x_11, x_11 is a writer or x_11 will not write a letter. For all x_11, if x_11 were a writer, then x_11 is writing a letter. There is at least one x_11 for which if x_11 writes a letter, then x_11 is a writer. Can we infer the following from them? There is at least one x_11 for which if x_11 writes a letter, then x_11 is a writer.
That is one of the premises. Therefore, the answer is yes.