Consider the following premises. If Mary were a nurse, then Sarah is a bartender. If Mary were bored, then it is late. If Sarah were a bartender, then Mary is bored. If it is late, then Sarah is a bartender. Can we infer the following from them? If we can, name the inference rule being used: If Mary were a nurse, then Mary is bored.
 From the fact that if Mary were bored, then it is late, and that if it is late, then Sarah is a bartender we can infer that if Mary were bored, then Sarah is a bartender via transitivity. From the fact that if Mary were bored, then Sarah is a bartender, and that if Sarah were a bartender, then Mary is bored we can infer that Mary is bored if and only if Sarah is a bartender via biconditional introduction. From the fact that Mary is bored if and only if Sarah is a bartender we can infer that if Sarah were a bartender, then Mary is bored via biconditional elimination. Finally, from the fact that if Mary were a nurse, then Sarah is a bartender, and that if Sarah were a bartender, then Mary is bored we can infer that if Mary were a nurse, then Mary is bored via transitivity. Therefore, the answer is yes.