Consider the following premises. For all y_4, y_4 is a nurse if and only if y_4 is an artist. There is at least one y_4 for which y_4 is a nurse if and only if y_4 is an artist. Can we infer the following from them? For all y_4, if is not true that y_4 is a nurse if and only if y_4 is an artist.
That contradicts the premises. Therefore the answer is no.