Consider the following premises. Richard is happy if and only if Susan is a cashier. It is raining if and only if Richard is happy. Susan is a cashier or James is fast. It is not raining. Can we infer the following from them? If we can, name the inference rule being used: James is not fast.
 From the fact that it is raining if and only if Richard is happy, and that it is not raining we can infer that Richard is not happy via biconditional elimination. From the fact that Richard is happy if and only if Susan is a cashier, and that Richard is not happy we can infer that Susan is not a cashier via biconditional elimination. Finally, from the fact that Susan is a cashier or James is fast, and that Susan is not a cashier we can infer that James is fast via disjunctive syllogism, which contradicts that James is not fast. Therefore, the answer is no.