Consider the following premises. For all x_4, x_4 is a writer. For all x_4, if x_4 writes a letter, then x_4 is a writer. For all x_4, if x_4 were a writer, then x_4 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 will write a letter.
 From the fact that for all x_4, if x_4 were a writer, then x_4 is writing a letter, and that for all x_4, if x_4 writes a letter, then x_4 is a writer we can infer that for all x_4, x_4 is a writer if and only if x_4 will write a letter via universal biconditional introduction. From the fact that for all x_4, x_4 is a writer if and only if x_4 will write a letter we can infer that for all x_4, if x_4 were a writer, then x_4 is writing a letter via universal biconditional elimination. Finally, from the fact that for all x_4, if x_4 were a writer, then x_4 is writing a letter, and that for all x_4, x_4 is a writer we can infer that for all x_4, x_4 will write a letter via universal modus ponens. Therefore, the answer is yes.