Consider the following premises. There is at least one x_7 for which x_7 is a writer or x_7 is not an artist. For all x_7, x_7 is an artist if and only if x_7 is a writer. Can we infer the following from them? For all x_7, if is not true that x_7 is a writer if and only if x_7 is an artist.
That contradicts the premises. Therefore the answer is no.