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