Theorem 6lt9

Description: 6 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015)

	Ref	Expression
Assertion	6lt9	⊢ 6 < 9

Proof

Step	Hyp	Ref	Expression
1		6lt7	⊢ 6 < 7
2		7lt9	⊢ 7 < 9
3		6re	⊢ 6 ∈ ℝ
4		7re	⊢ 7 ∈ ℝ
5		9re	⊢ 9 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 6 < 7 ∧ 7 < 9 ) → 6 < 9 )
7	1 2 6	mp2an	⊢ 6 < 9