Theorem absrei

Description: Absolute value of a real number. (Contributed by NM, 3-Aug-1999)

	Ref	Expression
Hypothesis	sqrtthi.1	$$⊢A\in ℝ$$
Assertion	absrei	$$⊢\left|A\right|=\sqrt{A^2}$$

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	$$⊢A\in ℝ$$
2		absre	$$⊢A\in ℝ\to \left|A\right|=\sqrt{A^2}$$
3	1 2	ax-mp	$$⊢\left|A\right|=\sqrt{A^2}$$