Consider the following premises. If it is late, then Jessica is a doctor. If Jessica plays tennis, then it is late. For all x, if x were a doctor, then x is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: Jessica is a doctor if and only if it is late.
 From the fact that for all x, if x were a doctor, then x is playing tennis we can infer that if Jessica were a doctor, then Jessica is playing tennis via universal instantiation. From the fact that if Jessica were a doctor, then Jessica is playing tennis, and that if Jessica plays tennis, then it is late we can infer that if Jessica were a doctor, then it is late via transitivity. Finally, from the fact that if Jessica were a doctor, then it is late, and that if it is late, then Jessica is a doctor we can infer that Jessica is a doctor if and only if it is late via biconditional introduction. Therefore, the answer is yes.