Consider the following premises. There is at least one z for which if z were sad, then z is driving a car. For all z, z will drive a car if and only if z is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which if z drives a car, then z is sad.
 From the fact that for all z, z will drive a car if and only if z is sad we can infer that for all z, if z drives a car, then z is sad via universal biconditional elimination. From the fact that for all z, if z drives a car, then z is sad, and that there is at least one z for which if z were sad, then z is driving a car we can infer that there is at least one z for which z will drive a car if and only if z is sad via existential biconditional introduction. Finally, from the fact that there is at least one z for which z will drive a car if and only if z is sad we can infer that there is at least one z for which if z drives a car, then z is sad via existential biconditional elimination. Therefore, the answer is yes.