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