Consider the following premises. For all x_1, x_1 is not a sailor. For all x_1, if x_1 were a bartender, then x_1 is a sailor. For all x_1, if x_1 were sad, then x_1 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, x_1 is not sad.
 From the fact that for all x_1, if x_1 were sad, then x_1 is a bartender, and that for all x_1, if x_1 were a bartender, then x_1 is a sailor we can infer that for all x_1, if x_1 were sad, then x_1 is a sailor via universal transitivity. Finally, from the fact that for all x_1, if x_1 were sad, then x_1 is a sailor, and that for all x_1, x_1 is not a sailor we can infer that for all x_1, x_1 is not sad via universal modus tollens. Therefore, the answer is yes.