Consider the following premises. For all x_1, x_1 is bored if and only if x_1 is fast. For all x_1, x_1 is bored if and only if x_1 is fast. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_1 for which the fact that x_1 were bored does not imply that x_1 is fast.
 From the fact that for all x_1, x_1 is bored if and only if x_1 is fast we can infer that for all x_1, if x_1 were fast, then x_1 is bored via universal biconditional elimination. From the fact that for all x_1, x_1 is bored if and only if x_1 is fast we can infer that for all x_1, if x_1 were bored, then x_1 is fast via universal biconditional elimination. From the fact that for all x_1, if x_1 were bored, then x_1 is fast, and that for all x_1, if x_1 were fast, then x_1 is bored we can infer that for all x_1, x_1 is bored if and only if x_1 is fast via universal biconditional introduction. Finally, from the fact that for all x_1, x_1 is bored if and only if x_1 is fast we can infer that for all x_1, if x_1 were bored, then x_1 is fast via universal biconditional elimination, which contradicts that There is at least one x_1 for which the fact that x_1 were bored does not imply that x_1 is fast. Therefore, the answer is no.