Consider the following premises. For all x_1, if x_1 drinks water, then x_1 is excited. There is at least one x_1 for which x_1 will not drink water. For all x_1, if x_1 were excited, 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, x_1 is excited.
 From the fact that for all x_1, if x_1 were excited, then x_1 is drinking water, and that for all x_1, if x_1 drinks water, then x_1 is excited we can infer that for all x_1, x_1 is excited if and only if x_1 will drink water via universal biconditional introduction. Finally, from the fact that for all x_1, x_1 is excited if and only if x_1 will drink water, and that there is at least one x_1 for which x_1 will not drink water we can infer that there is at least one x_1 for which x_1 is not excited via existential biconditional elimination, which contradicts that For all x_1, x_1 is excited. Therefore, the answer is no.