Consider the following premises. For all x_4, if x_4 were a scientist, then x_4 is a politician. For all x_4, x_4 is happy or x_4 is a scientist. For all x_4, if x_4 were happy, then x_4 is a politician. For all x_4, if x_4 were a politician, then x_4 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 is a cashier.
 From the fact that for all x_4, if x_4 were happy, then x_4 is a politician, that for all x_4, if x_4 were a scientist, then x_4 is a politician, and that for all x_4, x_4 is happy or x_4 is a scientist we can infer that for all x_4, x_4 is a politician via universal disjunction elimination. Finally, from the fact that for all x_4, if x_4 were a politician, then x_4 is a cashier, and that for all x_4, x_4 is a politician we can infer that for all x_4, x_4 is a cashier via universal modus ponens. Therefore, the answer is yes.