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Metamath Proof Explorer

Theorem absred

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

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

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