Consider the following premises. For all y_1, if y_1 writes a letter, then y_1 is an office clerk. For all y_1, if y_1 were an office clerk, then y_1 is a writer. For all y_1, y_1 is a writer if and only if y_1 will write a letter. Can we infer the following from them? There is at least one y_1 for which if is not true that y_1 is a writer if and only if y_1 will write a letter.
 From the fact that for all y_1, y_1 is a writer if and only if y_1 will write a letter we can infer that for all y_1, if y_1 were a writer, then y_1 is writing a letter. From the fact that for all y_1, if y_1 writes a letter, then y_1 is an office clerk, and that for all y_1, if y_1 were an office clerk, then y_1 is a writer we can infer that for all y_1, if y_1 writes a letter, then y_1 is a writer. Finally, from the fact that for all y_1, if y_1 were a writer, then y_1 is writing a letter, and that for all y_1, if y_1 writes a letter, then y_1 is a writer we can infer that for all y_1, y_1 is a writer if and only if y_1 will write a letter, which contradicts that There is at least one y_1 for which if is not true that y_1 is a writer if and only if y_1 will write a letter. Therefore, the answer is no.