Consider the following premises. For all y_4, y_4 will take a plane. Patricia is happy. For all y_4, if y_4 takes a plane, then y_4 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_4 for which y_4 will play a game and y_4 is happy.
 From the fact that for all y_4, if y_4 takes a plane, then y_4 is playing a game, and that for all y_4, y_4 will take a plane we can infer that for all y_4, y_4 will play a game via universal modus ponens. From the fact that Patricia is happy we can infer that there is at least one y_4 for which y_4 is happy via existential generalization. Finally, from the fact that for all y_4, y_4 will play a game, and that there is at least one y_4 for which y_4 is happy we can infer that there is at least one y_4 for which y_4 will play a game and y_4 is happy via existential conjunction. Therefore, the answer is yes.