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