Consider the following premises. For all x_11, x_11 will make tea if and only if x_11 will play squash. If Joseph makes tea, then Barbara is a cashier. For all x_11, x_11 will not play squash. If Barbara were a cashier, then Joseph is making tea. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not a cashier.
 From the fact that for all x_11, x_11 will make tea if and only if x_11 will play squash, and that for all x_11, x_11 will not play squash we can infer that for all x_11, x_11 will not make tea via universal biconditional elimination. From the fact that for all x_11, x_11 will not make tea we can infer that Joseph is not making tea via universal instantiation. From the fact that if Joseph makes tea, then Barbara is a cashier, and that if Barbara were a cashier, then Joseph is making tea we can infer that Joseph is making tea if and only if Barbara is a cashier via biconditional introduction. Finally, from the fact that Joseph is making tea if and only if Barbara is a cashier, and that Joseph is not making tea we can infer that Barbara is not a cashier via biconditional elimination. Therefore, the answer is yes.