Theorem 9pos

Description: The number 9 is positive. (Contributed by NM, 27-May-1999)

	Ref	Expression
Assertion	9pos	⊢ 0 < 9

Proof

Step	Hyp	Ref	Expression
1		8re	⊢ 8 ∈ ℝ
2		1re	⊢ 1 ∈ ℝ
3		8pos	⊢ 0 < 8
4		0lt1	⊢ 0 < 1
5	1 2 3 4	addgt0ii	⊢ 0 < ( 8 + 1 )
6		df-9	⊢ 9 = ( 8 + 1 )
7	5 6	breqtrri	⊢ 0 < 9