Consider the following premises. There is at least one y for which y will drive a car if and only if y will write a letter. For all y, if y writes a letter, then y is driving a car. Can we infer the following from them? For all y, if is not true that y will drive a car if and only if y will write a letter.
 From the fact that there is at least one y for which y will drive a car if and only if y will write a letter we can infer that there is at least one y for which if y drives a car, then y is writing a letter. Finally, from the fact that there is at least one y for which if y drives a car, then y is writing a letter, and that for all y, if y writes a letter, then y is driving a car we can infer that there is at least one y for which y will drive a car if and only if y will write a letter, which contradicts that For all y, if is not true that y will drive a car if and only if y will write a letter. Therefore, the answer is no.