Consider the following premises. John is sad. If John were sad, then Mary is working. Mary is working if and only if Joseph is happy. Can we infer the following from them? If we can, name the inference rule being used: Mary is not working.
 From the fact that John is sad we can infer that John is sad or Joseph is happy via addition. From the fact that Mary is working if and only if Joseph is happy we can infer that if Joseph were happy, then Mary is working via biconditional elimination. Finally, from the fact that if John were sad, then Mary is working, that if Joseph were happy, then Mary is working, and that John is sad or Joseph is happy we can infer that Mary is working via disjunction elimination, which contradicts that Mary is not working. Therefore, the answer is no.