Theorem 2lt10

Description: 2 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

	Ref	Expression
Assertion	2lt10	$$⊢2<10$$

Proof

Step	Hyp	Ref	Expression
1		2lt3	$$⊢2<3$$
2		3lt10	$$⊢3<10$$
3		2re	$$⊢2\in ℝ$$
4		3re	$$⊢3\in ℝ$$
5		10re	$$⊢10\in ℝ$$
6	3 4 5	lttri	$$⊢\left(2<3\wedge 3<10\right)\to 2<10$$
7	1 2 6	mp2an	$$⊢2<10$$