Consider the following premises. James is not fast. James is bored if and only if James is fast. For all x_12, if x_12 were fast, then x_12 is bored. Can we infer the following from them? If we can, name the inference rule being used: James is not bored.
 From the fact that for all x_12, if x_12 were fast, then x_12 is bored we can infer that if James were fast, then James is bored via universal instantiation. From the fact that James is bored if and only if James is fast we can infer that if James were bored, then James is fast via biconditional elimination. From the fact that if James were fast, then James is bored, and that if James were bored, then James is fast we can infer that James is fast if and only if James is bored via biconditional introduction. Finally, from the fact that James is fast if and only if James is bored, and that James is not fast we can infer that James is not bored via biconditional elimination. Therefore, the answer is yes.