Consider the following premises. David is a scientist. If it is late, then David is a scientist. If David were a scientist, then it is late. Can we infer the following from them? If we can, name the inference rule being used: It is not late.
 From the fact that if it is late, then David is a scientist, and that if David were a scientist, then it is late we can infer that it is late if and only if David is a scientist via biconditional introduction. From the fact that it is late if and only if David is a scientist we can infer that if David were a scientist, then it is late via biconditional elimination. Finally, from the fact that if David were a scientist, then it is late, and that David is a scientist we can infer that it is late via modus ponens, which contradicts that It is not late. Therefore, the answer is no.