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	$$⊢4\in ℝ$$
2		1re	$$⊢1\in ℝ$$
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	$$⊢0<5$$