Consider the following premises. John is a cashier or Elisabeth is not rich. If John were a cashier, then Elisabeth is playing squash. If it is overcast, then Elisabeth is rich. Can we infer the following from them? If we can, name the inference rule being used: If it is overcast, then Elisabeth is playing squash.
 From the fact that John is a cashier or Elisabeth is not rich we can infer that if Elisabeth were rich, then John is a cashier via rewriting. From the fact that if Elisabeth were rich, then John is a cashier, and that if John were a cashier, then Elisabeth is playing squash we can infer that if Elisabeth were rich, then Elisabeth is playing squash via transitivity. Finally, from the fact that if it is overcast, then Elisabeth is rich, and that if Elisabeth were rich, then Elisabeth is playing squash we can infer that if it is overcast, then Elisabeth is playing squash via transitivity. Therefore, the answer is yes.