Theorem 1lt8

Description: 1 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	1lt8	⊢ 1 < 8

Proof

Step	Hyp	Ref	Expression
1		1lt2	⊢ 1 < 2
2		2lt8	⊢ 2 < 8
3		1re	⊢ 1 ∈ ℝ
4		2re	⊢ 2 ∈ ℝ
5		8re	⊢ 8 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 1 < 2 ∧ 2 < 8 ) → 1 < 8 )
7	1 2 6	mp2an	⊢ 1 < 8