Theorem absred

Description: Absolute value of a real number. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	resqrcld.1	$$⊢\phi \to A\in ℝ$$
Assertion	absred	$$⊢\phi \to \left|A\right|=\sqrt{A^2}$$

Proof

Step	Hyp	Ref	Expression
1		resqrcld.1	$$⊢\phi \to A\in ℝ$$
2		absre	$$⊢A\in ℝ\to \left|A\right|=\sqrt{A^2}$$
3	1 2	syl	$$⊢\phi \to \left|A\right|=\sqrt{A^2}$$