Theorem absred

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

	Ref	Expression
Hypothesis	resqrcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	absred	⊢ ( 𝜑 → ( abs ‘ 𝐴 ) = ( √ ‘ ( 𝐴 ↑ 2 ) ) )

Proof

Step	Hyp	Ref	Expression
1		resqrcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		absre	⊢ ( 𝐴 ∈ ℝ → ( abs ‘ 𝐴 ) = ( √ ‘ ( 𝐴 ↑ 2 ) ) )
3	1 2	syl	⊢ ( 𝜑 → ( abs ‘ 𝐴 ) = ( √ ‘ ( 𝐴 ↑ 2 ) ) )