Theorem 3onn

Description: The ordinal 3 is a natural number. (Contributed by Mario Carneiro, 5-Jan-2016)

	Ref	Expression
Assertion	3onn	⊢ 3o ∈ ω

Proof

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