Consider the following premises. For all x_14, if x_14 were rich, then x_14 is not curious. For all x_14, x_14 is a mechanic. For all x_14, x_14 is not a mechanic. For all x_14, x_14 is rich if and only if x_14 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 is not a janitor.
 From the fact that for all x_14, x_14 is rich if and only if x_14 is a janitor we can infer that for all x_14, if x_14 were a janitor, then x_14 is rich via universal biconditional elimination. From the fact that for all x_14, x_14 is a mechanic we can infer that for all x_14, x_14 is a mechanic or x_14 is curious via universal addition. From the fact that for all x_14, x_14 is a mechanic or x_14 is curious, and that for all x_14, x_14 is not a mechanic we can infer that for all x_14, x_14 is curious via universal disjunctive syllogism. From the fact that for all x_14, if x_14 were rich, then x_14 is not curious, and that for all x_14, x_14 is curious we can infer that for all x_14, x_14 is not rich via universal modus tollens. Finally, from the fact that for all x_14, if x_14 were a janitor, then x_14 is rich, and that for all x_14, x_14 is not rich we can infer that for all x_14, x_14 is not a janitor via universal modus tollens. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.