Consider the following premises. For all y, y is excited or y will write a letter. For all y, y is not excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_3 for which y_3 will write a letter.
 From the fact that for all y, y is excited or y will write a letter, and that for all y, y is not excited we can infer that for all y, y will write a letter via universal disjunctive syllogism. From the fact that for all y, y will write a letter we can infer that Richard is writing a letter via universal instantiation. Finally, from the fact that Richard is writing a letter we can infer that there is at least one y_3 for which y_3 will write a letter via existential generalization. Therefore, the answer is yes.