Consider the following premises. It is raining if and only if David is cooking. It is raining if and only if David is cooking. Can we infer the following from them? The fact that it rains does not imply that David is cooking.
 From the fact that it is raining if and only if David is cooking we can infer that if David cooks, then it is raining. Finally, from the fact that it is raining if and only if David is cooking we can infer that if it rains, then David is cooking, which contradicts that The fact that it rains does not imply that David is cooking. Therefore, the answer is no.