Consider the following premises. For all x_3, x_3 is rich. There is at least one x_3 for which if x_3 were poor, then x_3 is not rich. For all x_3, x_3 is poor or x_3 is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 is a mechanic.
 From the fact that there is at least one x_3 for which if x_3 were poor, then x_3 is not rich, and that for all x_3, x_3 is rich we can infer that there is at least one x_3 for which x_3 is not poor via existential modus tollens. Finally, from the fact that for all x_3, x_3 is poor or x_3 is a mechanic, and that there is at least one x_3 for which x_3 is not poor we can infer that there is at least one x_3 for which x_3 is a mechanic via existential disjunctive syllogism. Therefore, the answer is yes.