Consider the following premises. There is at least one x_3 for which x_3 will not cook. For all x_3, if x_3 were a bartender, then x_3 is a scientist. For all x_3, if x_3 were a scientist, then x_3 is a bartender. For all x_3, if x_3 were a scientist, then x_3 is cooking. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, if x_3 were a bartender, then x_3 is a scientist.
That is one of the premises. Therefore, the answer is yes.