Description: A nonnegative number is its own absolute value. (Contributed by NM, 2-Aug-1999)
Ref | Expression | ||
---|---|---|---|
Hypothesis | sqrtthi.1 | ⊢ 𝐴 ∈ ℝ | |
Assertion | absidi | ⊢ ( 0 ≤ 𝐴 → ( abs ‘ 𝐴 ) = 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sqrtthi.1 | ⊢ 𝐴 ∈ ℝ | |
2 | absid | ⊢ ( ( 𝐴 ∈ ℝ ∧ 0 ≤ 𝐴 ) → ( abs ‘ 𝐴 ) = 𝐴 ) | |
3 | 1 2 | mpan | ⊢ ( 0 ≤ 𝐴 → ( abs ‘ 𝐴 ) = 𝐴 ) |