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Metamath Proof Explorer

Theorem absori

Description: The absolute value of a real number is either that number or its negative. (Contributed by NM, 30-Sep-1999)

Ref Expression
Hypothesis sqrtthi.1 ⊢ A ∈ ℝ
Assertion absori ⊢ A = A ∨ A = − A

Proof

Step Hyp Ref Expression
1 sqrtthi.1 ⊢ A ∈ ℝ
2 absor ⊢ A ∈ ℝ → A = A ∨ A = − A
3 1 2 ax-mp ⊢ A = A ∨ A = − A