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