Theorem 3lt10

Description: 3 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

	Ref	Expression
Assertion	3lt10	⊢ 3 < ; 1 0

Proof

Step	Hyp	Ref	Expression
1		3nn0	⊢ 3 ∈ ℕ0
2		3re	⊢ 3 ∈ ℝ
3		9re	⊢ 9 ∈ ℝ
4		3lt9	⊢ 3 < 9
5	2 3 4	ltleii	⊢ 3 ≤ 9
6	1 5	le9lt10	⊢ 3 < ; 1 0