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