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 ∈ ℝ
4		2re	⊢ 2 ∈ ℝ
5		9re	⊢ 9 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 1 < 2 ∧ 2 < 9 ) → 1 < 9 )
7	1 2 6	mp2an	⊢ 1 < 9