Theorem 1lt9

Description: 1 is less than 9. (Contributed by NM, 19-Oct-2012) (Revised by Mario Carneiro, 9-Mar-2015)

	Ref	Expression
Assertion	1lt9	$$⊢1<9$$

Proof

Step	Hyp	Ref	Expression
1		1lt2	$$⊢1<2$$
2		2lt9	$$⊢2<9$$
3		1re	$$⊢1\in ℝ$$
4		2re	$$⊢2\in ℝ$$
5		9re	$$⊢9\in ℝ$$
6	3 4 5	lttri	$$⊢\left(1<2\wedge 2<9\right)\to 1<9$$
7	1 2 6	mp2an	$$⊢1<9$$