Metamath Proof Explorer


Theorem absred

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

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

Proof

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