Consider the following premises. For all x_1, if x_1 were curious, then x_1 is a lawyer. For all x_1, if x_1 plays a game, then x_1 is a lawyer. There is at least one x_1 for which x_1 is curious. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_1 for which x_1 is a lawyer.
 From the fact that there is at least one x_1 for which x_1 is curious we can infer that there is at least one x_1 for which x_1 is curious or x_1 will play a game via existential addition. Finally, from the fact that for all x_1, if x_1 were curious, then x_1 is a lawyer, that for all x_1, if x_1 plays a game, then x_1 is a lawyer, and that there is at least one x_1 for which x_1 is curious or x_1 will play a game we can infer that there is at least one x_1 for which x_1 is a lawyer via existential disjunction elimination. Therefore, the answer is yes.