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| Description: 'Greater than' implies not equal. (Contributed by Mario Carneiro, 27-May-2016.) | 
| Ref | Expression | 
|---|---|
| ltd.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ) | 
| ltned.2 | ⊢ (𝜑 → 𝐴 < 𝐵) | 
| Ref | Expression | 
|---|---|
| ltned | ⊢ (𝜑 → 𝐴 ≠ 𝐵) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | ltd.1 | . . 3 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
| 2 | ltned.2 | . . 3 ⊢ (𝜑 → 𝐴 < 𝐵) | |
| 3 | 1, 2 | gtned 11396 | . 2 ⊢ (𝜑 → 𝐵 ≠ 𝐴) | 
| 4 | 3 | necomd 2996 | 1 ⊢ (𝜑 → 𝐴 ≠ 𝐵) | 
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