Consider the following premises. For all x_5, x_5 is rich if and only if x_5 is a mechanic. There is at least one x_5 for which x_5 is a mechanic. For all x_5, if x_5 makes tea, then x_5 is rich. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is not rich.
 From the fact that there is at least one x_5 for which x_5 is a mechanic we can infer that there is at least one x_5 for which x_5 is a mechanic or x_5 will make tea via existential addition. From the fact that for all x_5, x_5 is rich if and only if x_5 is a mechanic we can infer that for all x_5, if x_5 were a mechanic, then x_5 is rich via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 were a mechanic, then x_5 is rich, that for all x_5, if x_5 makes tea, then x_5 is rich, and that there is at least one x_5 for which x_5 is a mechanic or x_5 will make tea we can infer that there is at least one x_5 for which x_5 is rich via existential disjunction elimination, which contradicts that For all x_5, x_5 is not rich. Therefore, the answer is no.