Theorem absnidi

Description: A negative number is the negative of its own absolute value. (Contributed by NM, 2-Aug-1999)

	Ref	Expression
Hypothesis	sqrtthi.1	$$⊢A\in ℝ$$
Assertion	absnidi	$$⊢A\le 0\to \left|A\right|=-A$$

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	$$⊢A\in ℝ$$
2		absnid	$$⊢\left(A\in ℝ\wedge A\le 0\right)\to \left|A\right|=-A$$
3	1 2	mpan	$$⊢A\le 0\to \left|A\right|=-A$$