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