Consider the following premises. If Joseph were a sailor, then it is raining. If it rains, then it is sunny. If it rains, then Joseph is a sailor. If Charles reads a book, then Joseph is a sailor. Can we infer the following from them? If we can, name the inference rule being used: If Charles reads a book, then it is sunny.
 From the fact that if Joseph were a sailor, then it is raining, and that if it rains, then Joseph is a sailor we can infer that Joseph is a sailor if and only if it is raining via biconditional introduction. From the fact that Joseph is a sailor if and only if it is raining we can infer that if Joseph were a sailor, then it is raining via biconditional elimination. From the fact that if Joseph were a sailor, then it is raining, and that if it rains, then it is sunny we can infer that if Joseph were a sailor, then it is sunny via transitivity. Finally, from the fact that if Charles reads a book, then Joseph is a sailor, and that if Joseph were a sailor, then it is sunny we can infer that if Charles reads a book, then it is sunny via transitivity. Therefore, the answer is yes.