 Thoralf Skolem had considered the Skolemizations of formulas in prenex form as part of his proof of the Löwenheim–Skolem theorem (Skolem 1920).Herbrand worked with this dual notion of Herbrandization, generalized to apply to non-prenex formulas as well, in order to prove Herbrand's theorem (Herbrand 1930).The resulting formula is not necessarily equivalent to the original one.