Consider the following premises. There is at least one x for which if x makes tea, then x is fast. For all x, x is fast if and only if x is bored. For all x, x is fast if and only if x will make tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which if x makes tea, then x is bored.
 From the fact that for all x, x is fast if and only if x will make tea we can infer that for all x, if x were fast, then x is making tea via universal biconditional elimination. From the fact that for all x, if x were fast, then x is making tea, and that there is at least one x for which if x makes tea, then x is fast we can infer that there is at least one x for which x is fast if and only if x will make tea via existential biconditional introduction. From the fact that for all x, x is fast if and only if x is bored we can infer that for all x, if x were fast, then x is bored via universal biconditional elimination. From the fact that there is at least one x for which x is fast if and only if x will make tea we can infer that there is at least one x for which if x makes tea, then x is fast via existential biconditional elimination. Finally, from the fact that there is at least one x for which if x makes tea, then x is fast, and that for all x, if x were fast, then x is bored we can infer that there is at least one x for which if x makes tea, then x is bored via existential transitivity. Therefore, the answer is yes.