Theorem 10nn

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

	Ref	Expression
Assertion	10nn	⊢ ; 1 0 ∈ ℕ

Proof

Step	Hyp	Ref	Expression
1		9p1e10	⊢ ( 9 + 1 ) = ; 1 0
2		9nn	⊢ 9 ∈ ℕ
3		peano2nn	⊢ ( 9 ∈ ℕ → ( 9 + 1 ) ∈ ℕ )
4	2 3	ax-mp	⊢ ( 9 + 1 ) ∈ ℕ
5	1 4	eqeltrri	⊢ ; 1 0 ∈ ℕ