Consider the following premises. For all x_6, x_6 will play a game. For all x_6, if x_6 plays a game, then x_6 is rich. For all x_6, if x_6 were a carpenter, then x_6 is rich. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y is rich.
 From the fact that for all x_6, x_6 will play a game we can infer that for all x_6, x_6 will play a game or x_6 is a carpenter via universal addition. From the fact that for all x_6, if x_6 plays a game, then x_6 is rich, that for all x_6, if x_6 were a carpenter, then x_6 is rich, and that for all x_6, x_6 will play a game or x_6 is a carpenter we can infer that for all x_6, x_6 is rich via universal disjunction elimination. From the fact that for all x_6, x_6 is rich we can infer that William is rich via universal instantiation. Finally, from the fact that William is rich we can infer that there is at least one y for which y is rich via existential generalization. Therefore, the answer is yes.