Consider the following premises. If it is sunny, then Susan is a nurse. Linda is cooking if and only if it is sunny. If Susan were a nurse, then Linda is cooking. Can we infer the following from them? If we can, name the inference rule being used: If is not true that it is sunny if and only if Susan is a nurse.
 From the fact that Linda is cooking if and only if it is sunny we can infer that if Linda cooks, then it is sunny via biconditional elimination. From the fact that if Susan were a nurse, then Linda is cooking, and that if Linda cooks, then it is sunny we can infer that if Susan were a nurse, then it is sunny via transitivity. Finally, from the fact that if it is sunny, then Susan is a nurse, and that if Susan were a nurse, then it is sunny we can infer that it is sunny if and only if Susan is a nurse via biconditional introduction, which contradicts that If is not true that it is sunny if and only if Susan is a nurse. Therefore, the answer is no.