Theorem 5pos

Description: The number 5 is positive. (Contributed by NM, 27-May-1999)

	Ref	Expression
Assertion	5pos	⊢ 0 < 5

Proof

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