Theorem absrei

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

	Ref	Expression
Hypothesis	sqrtthi.1	⊢ 𝐴 ∈ ℝ
Assertion	absrei	⊢ ( abs ‘ 𝐴 ) = ( √ ‘ ( 𝐴 ↑ 2 ) )

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	⊢ 𝐴 ∈ ℝ
2		absre	⊢ ( 𝐴 ∈ ℝ → ( abs ‘ 𝐴 ) = ( √ ‘ ( 𝐴 ↑ 2 ) ) )
3	1 2	ax-mp	⊢ ( abs ‘ 𝐴 ) = ( √ ‘ ( 𝐴 ↑ 2 ) )