Consider the following premises. For all x, if x goes running, then x is drinking water. For all x, x will not go running. For all x, if x drinks water, then x is running. For all x, if x drinks water, then x is running. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will not drink water.
 From the fact that for all x, if x goes running, then x is drinking water, and that for all x, if x drinks water, then x is running we can infer that for all x, x will go running if and only if x will drink water via universal biconditional introduction. From the fact that for all x, x will go running if and only if x will drink water we can infer that for all x, if x goes running, then x is drinking water via universal biconditional elimination. From the fact that for all x, if x goes running, then x is drinking water, and that for all x, if x drinks water, then x is running we can infer that for all x, x will go running if and only if x will drink water via universal biconditional introduction. Finally, from the fact that for all x, x will go running if and only if x will drink water, and that for all x, x will not go running we can infer that for all x, x will not drink water via universal biconditional elimination. Therefore, the answer is yes.