Theorem 7lt9

Description: 7 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015)

	Ref	Expression
Assertion	7lt9	⊢ 7 < 9

Proof

Step	Hyp	Ref	Expression
1		7lt8	⊢ 7 < 8
2		8lt9	⊢ 8 < 9
3		7re	⊢ 7 ∈ ℝ
4		8re	⊢ 8 ∈ ℝ
5		9re	⊢ 9 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 7 < 8 ∧ 8 < 9 ) → 7 < 9 )
7	1 2 6	mp2an	⊢ 7 < 9