Consider the following premises. For all x_1, if x_1 drinks water, then x_1 is making tea. There is at least one x_1 for which if x_1 makes tea, then x_1 is curious. For all x_1, if x_1 were curious, then x_1 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, if is not true that x_1 will make tea if and only if x_1 will drink water.
 From the fact that there is at least one x_1 for which if x_1 makes tea, then x_1 is curious, and that for all x_1, if x_1 were curious, then x_1 is drinking water we can infer that there is at least one x_1 for which if x_1 makes tea, then x_1 is drinking water via existential transitivity. Finally, from the fact that there is at least one x_1 for which if x_1 makes tea, then x_1 is drinking water, and that for all x_1, if x_1 drinks water, then x_1 is making tea we can infer that there is at least one x_1 for which x_1 will make tea if and only if x_1 will drink water via existential biconditional introduction, which contradicts that For all x_1, if is not true that x_1 will make tea if and only if x_1 will drink water. Therefore, the answer is no.