Consider the following premises. It is snowing or Barbara is not a cashier. Richard is an astronaut if and only if Barbara is a cashier. Can we infer the following from them? If we can, name the inference rule being used: If Richard were an astronaut, then it is snowing.
 From the fact that it is snowing or Barbara is not a cashier we can infer that if Barbara were a cashier, then it is snowing via rewriting. From the fact that Richard is an astronaut if and only if Barbara is a cashier we can infer that if Richard were an astronaut, then Barbara is a cashier via biconditional elimination. Finally, from the fact that if Richard were an astronaut, then Barbara is a cashier, and that if Barbara were a cashier, then it is snowing we can infer that if Richard were an astronaut, then it is snowing via transitivity. Therefore, the answer is yes.