Consider the following premises. For all x_14, if x_14 were a politician, then x_14 is rich. For all x_14, x_14 will drink water or x_14 will not work. For all x_14, if x_14 drives a car, then x_14 is a politician. There is at least one x_14 for which if x_14 were rich, then x_14 is working. For all x_14, if x_14 drinks water, then x_14 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, if is not true that x_14 is a politician if and only if x_14 is rich.
 From the fact that for all x_14, if x_14 drinks water, then x_14 is driving a car, and that for all x_14, if x_14 drives a car, then x_14 is a politician we can infer that for all x_14, if x_14 drinks water, then x_14 is a politician via universal transitivity. From the fact that for all x_14, x_14 will drink water or x_14 will not work we can infer that for all x_14, if x_14 works, then x_14 is drinking water via universal rewriting. From the fact that for all x_14, if x_14 works, then x_14 is drinking water, and that for all x_14, if x_14 drinks water, then x_14 is a politician we can infer that for all x_14, if x_14 works, then x_14 is a politician via universal transitivity. From the fact that there is at least one x_14 for which if x_14 were rich, then x_14 is working, and that for all x_14, if x_14 works, then x_14 is a politician we can infer that there is at least one x_14 for which if x_14 were rich, then x_14 is a politician via existential transitivity. Finally, from the fact that for all x_14, if x_14 were a politician, then x_14 is rich, and that there is at least one x_14 for which if x_14 were rich, then x_14 is a politician we can infer that there is at least one x_14 for which x_14 is a politician if and only if x_14 is rich via existential biconditional introduction, which contradicts that For all x_14, if is not true that x_14 is a politician if and only if x_14 is rich. Therefore, the answer is no.