Consider the following premises. For all x_4, x_4 is an astronaut. For all x_4, x_4 will cook. For all x_4, if x_4 cooks, then x_4 is not an astronaut. Can we infer the following from them? For all x_4, if x_4 cooks, then x_4 is not an astronaut.
That is one of the premises. Therefore, the answer is yes.