Consider the following premises. For all x_2, x_2 will write a letter. For all x_2, x_2 is happy or x_2 will not write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 is happy.
 From the fact that for all x_2, x_2 is happy or x_2 will not write a letter we can infer that for all x_2, if x_2 writes a letter, then x_2 is happy via universal rewriting. Finally, from the fact that for all x_2, if x_2 writes a letter, then x_2 is happy, and that for all x_2, x_2 will write a letter we can infer that for all x_2, x_2 is happy via universal modus ponens. Therefore, the answer is yes.