Consider the following premises. For all x_9, x_9 is a mechanic. For all x_9, if x_9 were excited, then x_9 is rich. For all x_9, x_9 is a cashier or x_9 is excited. For all x_9, x_9 is rich or x_9 is not a cashier. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not rich.
 From the fact that for all x_9, x_9 is rich or x_9 is not a cashier we can infer that for all x_9, if x_9 were a cashier, then x_9 is rich via universal rewriting. Finally, from the fact that for all x_9, if x_9 were a cashier, then x_9 is rich, that for all x_9, if x_9 were excited, then x_9 is rich, and that for all x_9, x_9 is a cashier or x_9 is excited we can infer that for all x_9, x_9 is rich via universal disjunction elimination, which contradicts that Patricia is not rich. Therefore, the answer is no.