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Metamath Proof Explorer

Theorem 10nn

Description: 10 is a positive integer. (Contributed by NM, 8-Nov-2012) (Revised by AV, 6-Sep-2021)

		Ref	Expression
	Assertion	10nn	$⊢ 10 \in ℕ$

Step	Hyp	Ref	Expression
1		9p1e10	$⊢ 9 + 1 = 10$
2		9nn	$⊢ 9 \in ℕ$
3		peano2nn	$⊢ 9 \in ℕ \to 9 + 1 \in ℕ$
4	2 3	ax-mp	$⊢ 9 + 1 \in ℕ$
5	1 4	eqeltrri	$⊢ 10 \in ℕ$