Consider the following premises. Susan is a sailor if and only if Susan is playing tennis. For all x_2, x_2 is a sailor if and only if x_2 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: Susan is playing tennis if and only if Susan is a sailor.
 From the fact that for all x_2, x_2 is a sailor if and only if x_2 will play tennis we can infer that Susan is a sailor if and only if Susan is playing tennis via universal instantiation. From the fact that Susan is a sailor if and only if Susan is playing tennis we can infer that if Susan were a sailor, then Susan is playing tennis via biconditional elimination. From the fact that Susan is a sailor if and only if Susan is playing tennis we can infer that if Susan plays tennis, then Susan is a sailor via biconditional elimination. Finally, from the fact that if Susan plays tennis, then Susan is a sailor, and that if Susan were a sailor, then Susan is playing tennis we can infer that Susan is playing tennis if and only if Susan is a sailor via biconditional introduction. Therefore, the answer is yes.