Consider the following premises. Elisabeth is a scientist or David is not rich. If Elisabeth plays tennis, then David is rich. If Elisabeth were a scientist, then Elisabeth is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: David is rich if and only if Elisabeth is a scientist.
 From the fact that Elisabeth is a scientist or David is not rich we can infer that if David were rich, then Elisabeth is a scientist via rewriting. From the fact that if Elisabeth were a scientist, then Elisabeth is playing tennis, and that if Elisabeth plays tennis, then David is rich we can infer that if Elisabeth were a scientist, then David is rich via transitivity. Finally, from the fact that if David were rich, then Elisabeth is a scientist, and that if Elisabeth were a scientist, then David is rich we can infer that David is rich if and only if Elisabeth is a scientist via biconditional introduction. Therefore, the answer is yes.