Theorem halfnneg2

Description: A number is nonnegative iff its half is nonnegative. (Contributed by NM, 9-Dec-2005)

	Ref	Expression
Assertion	halfnneg2	$$⊢A\in ℝ\to \left(0\le A\leftrightarrow 0\le \frac{A}{2}\right)$$

Proof

Step	Hyp	Ref	Expression
1		2re	$$⊢2\in ℝ$$
2		2pos	$$⊢0<2$$
3		ge0div	$$⊢\left(A\in ℝ\wedge 2\in ℝ\wedge 0<2\right)\to \left(0\le A\leftrightarrow 0\le \frac{A}{2}\right)$$
4	1 2 3	mp3an23	$$⊢A\in ℝ\to \left(0\le A\leftrightarrow 0\le \frac{A}{2}\right)$$