Theorem 1lt10

Description: 1 is less than 10. (Contributed by NM, 7-Nov-2012) (Revised by Mario Carneiro, 9-Mar-2015) (Revised by AV, 8-Sep-2021)

	Ref	Expression
Assertion	1lt10	$$⊢1<10$$

Proof

Step	Hyp	Ref	Expression
1		1lt2	$$⊢1<2$$
2		2lt10	$$⊢2<10$$
3		1re	$$⊢1\in ℝ$$
4		2re	$$⊢2\in ℝ$$
5		10re	$$⊢10\in ℝ$$
6	3 4 5	lttri	$$⊢\left(1<2\wedge 2<10\right)\to 1<10$$
7	1 2 6	mp2an	$$⊢1<10$$