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	$$⊢3<10$$

Proof

Step	Hyp	Ref	Expression
1		3nn0	$$⊢3\in {\mathbb{N}}_0$$
2		3re	$$⊢3\in ℝ$$
3		9re	$$⊢9\in ℝ$$
4		3lt9	$$⊢3<9$$
5	2 3 4	ltleii	$$⊢3\le 9$$
6	1 5	le9lt10	$$⊢3<10$$