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