Theorem absidi

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

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

Proof

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