Consider the following premises. For all x_3, x_3 is not a mechanic. For all x_3, x_3 is a mechanic if and only if x_3 is a cashier. For all x_3, x_3 is a cashier if and only if x_3 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 is not a soldier.
 From the fact that for all x_3, x_3 is a mechanic if and only if x_3 is a cashier, and that for all x_3, x_3 is not a mechanic we can infer that for all x_3, x_3 is not a cashier via universal biconditional elimination. Finally, from the fact that for all x_3, x_3 is a cashier if and only if x_3 is a soldier, and that for all x_3, x_3 is not a cashier we can infer that for all x_3, x_3 is not a soldier via universal biconditional elimination. Therefore, the answer is yes.