Description: Comparison of a number and its negative to zero. (Contributed by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | leidd.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℝ ) | |
Assertion | lt0neg2d | ⊢ ( 𝜑 → ( 0 < 𝐴 ↔ - 𝐴 < 0 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | leidd.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℝ ) | |
2 | lt0neg2 | ⊢ ( 𝐴 ∈ ℝ → ( 0 < 𝐴 ↔ - 𝐴 < 0 ) ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 0 < 𝐴 ↔ - 𝐴 < 0 ) ) |