Consider the following premises. For all x_4, if x_4 were excited, then x_4 is playing a game. For all x_4, x_4 is excited or x_4 is a scientist. For all x_4, if x_4 were a scientist, then x_4 is playing a game. There is at least one x_4 for which x_4 is an electrician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 will play a game and x_4 is an electrician.
 From the fact that for all x_4, if x_4 were excited, then x_4 is playing a game, that for all x_4, if x_4 were a scientist, then x_4 is playing a game, and that for all x_4, x_4 is excited or x_4 is a scientist we can infer that for all x_4, x_4 will play a game via universal disjunction elimination. Finally, from the fact that for all x_4, x_4 will play a game, and that there is at least one x_4 for which x_4 is an electrician we can infer that there is at least one x_4 for which x_4 will play a game and x_4 is an electrician via existential conjunction. Therefore, the answer is yes.