Consider the following premises. For all x_10, x_10 will not write a letter. It is late if and only if Mary is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: It is not late.
 From the fact that for all x_10, x_10 will not write a letter we can infer that Mary is not writing a letter via universal instantiation. From the fact that it is late if and only if Mary is writing a letter we can infer that if it is late, then Mary is writing a letter via biconditional elimination. Finally, from the fact that if it is late, then Mary is writing a letter, and that Mary is not writing a letter we can infer that it is not late via modus tollens. Therefore, the answer is yes.