Consider the following premises. For all x_6, if x_6 makes tea, then x_6 is a cashier. For all x_6, x_6 is a cashier. There is at least one x_6 for which if x_6 were a cashier, then x_6 is making tea. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not make tea.
 From the fact that there is at least one x_6 for which if x_6 were a cashier, then x_6 is making tea, and that for all x_6, if x_6 makes tea, then x_6 is a cashier we can infer that there is at least one x_6 for which x_6 is a cashier if and only if x_6 will make tea via existential biconditional introduction. From the fact that there is at least one x_6 for which x_6 is a cashier if and only if x_6 will make tea we can infer that there is at least one x_6 for which if x_6 were a cashier, then x_6 is making tea via existential biconditional elimination. Finally, from the fact that there is at least one x_6 for which if x_6 were a cashier, then x_6 is making tea, and that for all x_6, x_6 is a cashier we can infer that there is at least one x_6 for which x_6 will make tea via existential modus ponens, which contradicts that For all x_6, x_6 will not make tea. Therefore, the answer is no.