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 ) ) ) |
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 ) ) ) |