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Metamath Proof Explorer

Theorem lt0neg1dd

Description: If a number is negative, its negative is positive. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Hypotheses lt0neg1dd.1 ⊢ φ → A ∈ ℝ
lt0neg1dd.2 ⊢ φ → A < 0
Assertion lt0neg1dd ⊢ φ → 0 < − A

Proof

Step Hyp Ref Expression
1 lt0neg1dd.1 ⊢ φ → A ∈ ℝ
2 lt0neg1dd.2 ⊢ φ → A < 0
3 1 lt0neg1d ⊢ φ → A < 0 ↔ 0 < − A
4 2 3 mpbid ⊢ φ → 0 < − A