Consider the following premises. For all x, if x plays tennis, then x is climbing a mountain. For all x, if x climbs a mountain, then x is playing tennis. For all x, if x climbs a mountain, then x is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: If Richard plays tennis, then Richard is climbing a mountain.
 From the fact that for all x, if x climbs a mountain, then x is playing tennis, and that for all x, if x plays tennis, then x is climbing a mountain we can infer that for all x, x will climb a mountain if and only if x will play tennis via universal biconditional introduction. From the fact that for all x, x will climb a mountain if and only if x will play tennis we can infer that for all x, if x plays tennis, then x is climbing a mountain via universal biconditional elimination. From the fact that for all x, if x climbs a mountain, then x is playing tennis, and that for all x, if x plays tennis, then x is climbing a mountain we can infer that for all x, x will climb a mountain if and only if x will play tennis via universal biconditional introduction. From the fact that for all x, x will climb a mountain if and only if x will play tennis we can infer that Richard is climbing a mountain if and only if Richard is playing tennis via universal instantiation. Finally, from the fact that Richard is climbing a mountain if and only if Richard is playing tennis we can infer that if Richard plays tennis, then Richard is climbing a mountain via biconditional elimination. Therefore, the answer is yes.