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| Mirrors > Home > MPE Home > Th. List > ltneii | Structured version Visualization version GIF version | ||
| Description: 'Greater than' implies not equal. (Contributed by Mario Carneiro, 16-Sep-2015.) |
| Ref | Expression |
|---|---|
| lt.1 | ⊢ 𝐴 ∈ ℝ |
| ltneii.2 | ⊢ 𝐴 < 𝐵 |
| Ref | Expression |
|---|---|
| ltneii | ⊢ 𝐴 ≠ 𝐵 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | lt.1 | . . 3 ⊢ 𝐴 ∈ ℝ | |
| 2 | ltneii.2 | . . 3 ⊢ 𝐴 < 𝐵 | |
| 3 | 1, 2 | gtneii 11373 | . 2 ⊢ 𝐵 ≠ 𝐴 |
| 4 | 3 | necomi 2995 | 1 ⊢ 𝐴 ≠ 𝐵 |
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