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 < ; 1 0

Proof

Step	Hyp	Ref	Expression
1		1lt2	⊢ 1 < 2
2		2lt10	⊢ 2 < ; 1 0
3		1re	⊢ 1 ∈ ℝ
4		2re	⊢ 2 ∈ ℝ
5		10re	⊢ ; 1 0 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 1 < 2 ∧ 2 < ; 1 0 ) → 1 < ; 1 0 )
7	1 2 6	mp2an	⊢ 1 < ; 1 0