Theorem 8lt10

Description: 8 is less than 10. (Contributed by Mario Carneiro, 8-Feb-2015) (Revised by AV, 8-Sep-2021)

	Ref	Expression
Assertion	8lt10	$$⊢8<10$$

Proof

Step	Hyp	Ref	Expression
1		8lt9	$$⊢8<9$$
2		9lt10	$$⊢9<10$$
3		8re	$$⊢8\in ℝ$$
4		9re	$$⊢9\in ℝ$$
5		10re	$$⊢10\in ℝ$$
6	3 4 5	lttri	$$⊢\left(8<9\wedge 9<10\right)\to 8<10$$
7	1 2 6	mp2an	$$⊢8<10$$