Theorem absori

Description: The absolute value of a real number is either that number or its negative. (Contributed by NM, 30-Sep-1999)

	Ref	Expression
Hypothesis	sqrtthi.1	$$⊢A\in ℝ$$
Assertion	absori	$$⊢\left(\left|A\right|=A\vee \left|A\right|=-A\right)$$

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	$$⊢A\in ℝ$$
2		absor	$$⊢A\in ℝ\to \left(\left|A\right|=A\vee \left|A\right|=-A\right)$$
3	1 2	ax-mp	$$⊢\left(\left|A\right|=A\vee \left|A\right|=-A\right)$$