Consider the following premises. For all x_8, x_8 is poor if and only if x_8 is a bartender. For all x_8, x_8 is not a bartender. For all x_8, x_8 is poor if and only if x_8 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_8 for which x_8 is a mechanic.
 From the fact that for all x_8, x_8 is poor if and only if x_8 is a bartender, and that for all x_8, x_8 is not a bartender we can infer that for all x_8, x_8 is not poor via universal biconditional elimination. From the fact that for all x_8, x_8 is poor if and only if x_8 is a mechanic we can infer that for all x_8, if x_8 were a mechanic, then x_8 is poor via universal biconditional elimination. Finally, from the fact that for all x_8, if x_8 were a mechanic, then x_8 is poor, and that for all x_8, x_8 is not poor we can infer that for all x_8, x_8 is not a mechanic via universal modus tollens, which contradicts that There is at least one x_8 for which x_8 is a mechanic. Therefore, the answer is no.