Consider the following premises. Robert is sad if and only if John is writing a letter. Robert is sad if and only if Patricia is rich. Patricia is not rich. Robert is sleeping. Can we infer the following from them? If we can, name the inference rule being used: John is not writing a letter.
 From the fact that Robert is sad if and only if Patricia is rich, and that Patricia is not rich we can infer that Robert is not sad via biconditional elimination. Finally, from the fact that Robert is sad if and only if John is writing a letter, and that Robert is not sad we can infer that John is not writing a letter via biconditional elimination. Therefore, the answer is yes.