Theorem 4onn

Description: The ordinal 4 is a natural number. (Contributed by Mario Carneiro, 5-Jan-2016)

	Ref	Expression
Assertion	4onn	⊢ 4o ∈ ω

Proof

Step	Hyp	Ref	Expression
1		df-4o	⊢ 4o = suc 3o
2		3onn	⊢ 3o ∈ ω
3		peano2	⊢ ( 3o ∈ ω → suc 3o ∈ ω )
4	2 3	ax-mp	⊢ suc 3o ∈ ω
5	1 4	eqeltri	⊢ 4o ∈ ω