Theorem 4onn

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

	Ref	Expression
Assertion	4onn	$$⊢4_{𝑜}\in \mathrm{\omega }$$

Proof

Step	Hyp	Ref	Expression
1		df-4o	$$⊢4_{𝑜}=\mathrm{suc}{3}_{𝑜}$$
2		3onn	$$⊢3_{𝑜}\in \mathrm{\omega }$$
3		peano2	$$⊢3_{𝑜}\in \mathrm{\omega }\to \mathrm{suc}{3}_{𝑜}\in \mathrm{\omega }$$
4	2 3	ax-mp	$$⊢\mathrm{suc}{3}_{𝑜}\in \mathrm{\omega }$$
5	1 4	eqeltri	$$⊢4_{𝑜}\in \mathrm{\omega }$$