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Metamath Proof Explorer

Theorem absord

Description: The absolute value of a real number is either that number or its negative. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis resqrcld.1 ⊢ φ → A ∈ ℝ
Assertion absord ⊢ φ → A = A ∨ A = − A

Proof

Step Hyp Ref Expression
1 resqrcld.1 ⊢ φ → A ∈ ℝ
2 absor ⊢ A ∈ ℝ → A = A ∨ A = − A
3 1 2 syl ⊢ φ → A = A ∨ A = − A