Consider the following premises. For all x_6, x_6 will play tennis if and only if x_6 is a bartender. For all x_6, x_6 will take a plane or x_6 will play tennis. For all x_6, x_6 will not take a plane. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is not a bartender.
 From the fact that for all x_6, x_6 will take a plane or x_6 will play tennis, and that for all x_6, x_6 will not take a plane we can infer that for all x_6, x_6 will play tennis via universal disjunctive syllogism. From the fact that for all x_6, x_6 will play tennis if and only if x_6 is a bartender we can infer that for all x_6, if x_6 plays tennis, then x_6 is a bartender via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 plays tennis, then x_6 is a bartender, and that for all x_6, x_6 will play tennis we can infer that for all x_6, x_6 is a bartender via universal modus ponens, which contradicts that There is at least one x_6 for which x_6 is not a bartender. Therefore, the answer is no.