Consider the following premises. If Thomas were happy, then it is sunny. If it is sunny, then Joseph is sleeping. If Robert were an artist, then Thomas is happy. Robert is an artist or Joseph is not sleeping. Can we infer the following from them? If we can, name the inference rule being used: Joseph is sleeping if and only if Robert is an artist.
 From the fact that if Thomas were happy, then it is sunny, and that if it is sunny, then Joseph is sleeping we can infer that if Thomas were happy, then Joseph is sleeping via transitivity. From the fact that if Robert were an artist, then Thomas is happy, and that if Thomas were happy, then Joseph is sleeping we can infer that if Robert were an artist, then Joseph is sleeping via transitivity. From the fact that Robert is an artist or Joseph is not sleeping we can infer that if Joseph sleeps, then Robert is an artist via rewriting. Finally, from the fact that if Joseph sleeps, then Robert is an artist, and that if Robert were an artist, then Joseph is sleeping we can infer that Joseph is sleeping if and only if Robert is an artist via biconditional introduction. Therefore, the answer is yes.