Theorem 6lt8

Description: 6 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	6lt8	⊢ 6 < 8

Proof

Step	Hyp	Ref	Expression
1		6lt7	⊢ 6 < 7
2		7lt8	⊢ 7 < 8
3		6re	⊢ 6 ∈ ℝ
4		7re	⊢ 7 ∈ ℝ
5		8re	⊢ 8 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 6 < 7 ∧ 7 < 8 ) → 6 < 8 )
7	1 2 6	mp2an	⊢ 6 < 8