Theorem 3pos

Description: The number 3 is positive. (Contributed by NM, 27-May-1999)

	Ref	Expression
Assertion	3pos	⊢ 0 < 3

Proof

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