Consider the following premises. For all y_2, if y_2 were excited, then y_2 is reading a book. There is at least one y_2 for which y_2 is excited if and only if y_2 will write a letter. For all y_2, y_2 will write a letter if and only if y_2 will read a book. Can we infer the following from them? If we can, name the inference rule being used: For all y_2, if is not true that y_2 will write a letter if and only if y_2 will read a book.
That contradicts the premises. Therefore the answer is no.