Consider the following premises. For all x_7, x_7 will drive a car. For all x_7, if x_7 were a bartender, then x_7 is not cooking. For all x_7, x_7 will drive a car if and only if x_7 will cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 is a bartender.
 From the fact that for all x_7, x_7 will drive a car if and only if x_7 will cook we can infer that for all x_7, if x_7 drives a car, then x_7 is cooking via universal biconditional elimination. From the fact that for all x_7, if x_7 drives a car, then x_7 is cooking, and that for all x_7, x_7 will drive a car we can infer that for all x_7, x_7 will cook via universal modus ponens. Finally, from the fact that for all x_7, if x_7 were a bartender, then x_7 is not cooking, and that for all x_7, x_7 will cook we can infer that for all x_7, x_7 is not a bartender via universal modus tollens, which contradicts that There is at least one x_7 for which x_7 is a bartender. Therefore, the answer is no.