Consider the following premises. For all x_2, x_2 is rich or x_2 will not take a plane. For all x_2, x_2 will take a plane if and only if x_2 is rich. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which if is not true that x_2 will take a plane if and only if x_2 is rich.
 From the fact that for all x_2, x_2 will take a plane if and only if x_2 is rich we can infer that for all x_2, if x_2 were rich, then x_2 is taking a plane via universal biconditional elimination. From the fact that for all x_2, x_2 is rich or x_2 will not take a plane we can infer that for all x_2, if x_2 takes a plane, then x_2 is rich via universal rewriting. Finally, from the fact that for all x_2, if x_2 takes a plane, then x_2 is rich, and that for all x_2, if x_2 were rich, then x_2 is taking a plane we can infer that for all x_2, x_2 will take a plane if and only if x_2 is rich via universal biconditional introduction, which contradicts that There is at least one x_2 for which if is not true that x_2 will take a plane if and only if x_2 is rich. Therefore, the answer is no.