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| Mirrors > Home > MPE Home > Th. List > neii | Structured version Visualization version GIF version | ||
| Description: Inference associated with df-ne 2941. (Contributed by BJ, 7-Jul-2018.) |
| Ref | Expression |
|---|---|
| neii.1 | ⊢ 𝐴 ≠ 𝐵 |
| Ref | Expression |
|---|---|
| neii | ⊢ ¬ 𝐴 = 𝐵 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | neii.1 | . 2 ⊢ 𝐴 ≠ 𝐵 | |
| 2 | df-ne 2941 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵) | |
| 3 | 1, 2 | mpbi 230 | 1 ⊢ ¬ 𝐴 = 𝐵 |
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