Consider the following premises. For all x, x will work if and only if x is rich. For all x, x will work or x will not play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x, if x plays tennis, then x is rich.
 From the fact that for all x, x will work or x will not play tennis we can infer that for all x, if x plays tennis, then x is working via universal rewriting. From the fact that for all x, x will work if and only if x is rich we can infer that for all x, if x works, then x is rich via universal biconditional elimination. Finally, from the fact that for all x, if x plays tennis, then x is working, and that for all x, if x works, then x is rich we can infer that for all x, if x plays tennis, then x is rich via universal transitivity. Therefore, the answer is yes.