Consider the following premises. Robert is a nurse or it is windy. It is windy if and only if it is cloudy. Robert is a nurse if and only if it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: It is cloudy.
 From the fact that it is windy if and only if it is cloudy we can infer that if it is windy, then it is cloudy via biconditional elimination. From the fact that Robert is a nurse if and only if it is cloudy we can infer that if Robert were a nurse, then it is cloudy via biconditional elimination. Finally, from the fact that if Robert were a nurse, then it is cloudy, that if it is windy, then it is cloudy, and that Robert is a nurse or it is windy we can infer that it is cloudy via disjunction elimination. Therefore, the answer is yes.