Consider the following premises. For all y, if y writes a letter, then y is a writer. There is at least one y for which if y were a writer, then y is taking a plane. For all y, y will write a letter or y will not take a plane. Can we infer the following from them? There is at least one y for which y will write a letter if and only if y will take a plane.
 From the fact that for all y, y will write a letter or y will not take a plane we can infer that for all y, if y takes a plane, then y is writing a letter. From the fact that for all y, if y writes a letter, then y is a writer, and that there is at least one y for which if y were a writer, then y is taking a plane we can infer that there is at least one y for which if y writes a letter, then y is taking a plane. Finally, from the fact that there is at least one y for which if y writes a letter, then y is taking a plane, and that for all y, if y takes a plane, then y is writing a letter we can infer that there is at least one y for which y will write a letter if and only if y will take a plane. Therefore, the answer is yes.