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Metamath Proof Explorer

Theorem 3onn

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

		Ref	Expression
	Assertion	3onn	$⊢ 3_{𝑜} \in ω$

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