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