Theorem 5lt10

Description: 5 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

	Ref	Expression
Assertion	5lt10	$$⊢5<10$$

Proof

Step	Hyp	Ref	Expression
1		5lt6	$$⊢5<6$$
2		6lt10	$$⊢6<10$$
3		5re	$$⊢5\in ℝ$$
4		6re	$$⊢6\in ℝ$$
5		10re	$$⊢10\in ℝ$$
6	3 4 5	lttri	$$⊢\left(5<6\wedge 6<10\right)\to 5<10$$
7	1 2 6	mp2an	$$⊢5<10$$