Consider the following premises. For all x_4, if x_4 works, then x_4 is a police officer. For all x_4, x_4 is a police officer if and only if x_4 is a lawyer. There is at least one x_4 for which if x_4 were a lawyer, then x_4 is working. Can we infer the following from them? For all x_4, if is not true that x_4 is a police officer if and only if x_4 will work.
That contradicts the premises. Therefore the answer is no.