Theorem 6lt10

Description: 6 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

	Ref	Expression
Assertion	6lt10	$$⊢6<10$$

Proof

Step	Hyp	Ref	Expression
1		6lt7	$$⊢6<7$$
2		7lt10	$$⊢7<10$$
3		6re	$$⊢6\in ℝ$$
4		7re	$$⊢7\in ℝ$$
5		10re	$$⊢10\in ℝ$$
6	3 4 5	lttri	$$⊢\left(6<7\wedge 7<10\right)\to 6<10$$
7	1 2 6	mp2an	$$⊢6<10$$