 In detail, proving that the ZF axioms, apart from the comprehension axiom, are true in L, amounts to showing that, roughly speaking, any set with a property P that a ZF axiom asserts to exist, can be seen to exist in L by considering the relativization PL of the property P to L. (A property P is relativized to an inner model M by replacing every quantifier ∃xφ by ∃x(x ∈ M ∧ φ) and every quantifier ∀xφ by ∀x(x ∈ M→ φ).) As for the comprehension axiom, verifying it requires showing that the set asserted to exist is constructed at a particular successor level Lα + 1. Proving this requires an important principle of set theory which in modern terminology is called the Levy (or ZF) Reflection Principle. This principle says that any statement in the language of ZF which is true in V is already true on some level of any continuously increasing hierarchy such as L. (For the history of this principle, see Kanamori 2006.) The Levy Reflection Principle gives the level α at which the elements of the set are all constructed. Gödel did not actually have the Levy Reflection Principle but used the argument behind the proof of the principle.