Consider the following premises. There is at least one x for which if x makes tea, then x is fast. For all x, x will make tea or x is not fast. For all x, x will not 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 x is not fast.
 From the fact that for all x, x will make tea or x is not fast we can infer that for all x, if x were fast, then x is making tea via universal rewriting. 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 making tea we can infer that there is at least one x for which x will make tea if and only if x is fast via existential biconditional introduction. Finally, from the fact that there is at least one x for which x will make tea if and only if x is fast, and that for all x, x will not make tea we can infer that there is at least one x for which x is not fast via existential biconditional elimination. Therefore, the answer is yes.