Consider the following premises. There is at least one x_6 for which if x_6 were an astronaut, then x_6 is an artist. For all x_6, x_6 is an artist if and only if x_6 is a lawyer. For all x_6, if x_6 were a lawyer, then x_6 is an astronaut. Can we infer the following from them? For all x_6, if is not true that x_6 is a lawyer if and only if x_6 is an artist.
That contradicts the premises. Therefore the answer is no.