Consider the following premises. For all y_2, if y_2 were sad, then y_2 is working. There is at least one y_2 for which if y_2 works, then y_2 is sad. Can we infer the following from them? For all y_2, if is not true that y_2 will work if and only if y_2 is sad.
That contradicts the premises. Therefore the answer is no.