Theorem 5lt10

Description: 5 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	5lt10	$$⊢5<10$$

Proof

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