Consider the following premises. For all x_2, x_2 is happy if and only if x_2 is poor. For all x_2, if x_2 works, then x_2 is happy. There is at least one x_2 for which x_2 is poor if and only if x_2 will work. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, the fact that x_2 works does not imply that x_2 is poor.
That contradicts the premises. Therefore the answer is no.