Theorem 7pos

Description: The number 7 is positive. (Contributed by NM, 27-May-1999)

	Ref	Expression
Assertion	7pos	⊢ 0 < 7

Proof

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