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