Theorem 4.4: A natural number is a set.

Proof: Let n be a natural number. We proceed by induction on n.

Anchor: 0 = { } is a set by Axiom 4.

Induction: Assume that n is a set. Then by Definition 4.3,

n is a set by assumption.

so it is a set by Axioms 3 and 1, and so n + 1, their union, is a set by Axiom 2.