Consider the following premises. There is at least one x_15 for which if x_15 were a doctor, then x_15 is taking a plane. For all x_15, if x_15 drives a car, then x_15 is a cashier. For all x_15, x_15 is a doctor or x_15 is not a cashier. For all x_15, x_15 will drive a car if and only if x_15 will 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_15 for which x_15 will take a plane if and only if x_15 is a cashier.
 From the fact that for all x_15, x_15 is a doctor or x_15 is not a cashier we can infer that for all x_15, if x_15 were a cashier, then x_15 is a doctor via universal rewriting. From the fact that for all x_15, x_15 will drive a car if and only if x_15 will take a plane we can infer that for all x_15, if x_15 takes a plane, then x_15 is driving a car via universal biconditional elimination. From the fact that for all x_15, if x_15 takes a plane, then x_15 is driving a car, and that for all x_15, if x_15 drives a car, then x_15 is a cashier we can infer that for all x_15, if x_15 takes a plane, then x_15 is a cashier via universal transitivity. From the fact that for all x_15, if x_15 were a cashier, then x_15 is a doctor, and that there is at least one x_15 for which if x_15 were a doctor, then x_15 is taking a plane we can infer that there is at least one x_15 for which if x_15 were a cashier, then x_15 is taking a plane via existential transitivity. Finally, from the fact that for all x_15, if x_15 takes a plane, then x_15 is a cashier, and that there is at least one x_15 for which if x_15 were a cashier, then x_15 is taking a plane we can infer that there is at least one x_15 for which x_15 will take a plane if and only if x_15 is a cashier via existential biconditional introduction. Therefore, the answer is yes.