| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > neqne | Structured version Visualization version GIF version | ||
| Description: From non-equality to inequality. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
| Ref | Expression |
|---|---|
| neqne | ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | id 22 | . 2 ⊢ (¬ 𝐴 = 𝐵 → ¬ 𝐴 = 𝐵) | |
| 2 | 1 | neqned 2947 | 1 ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵) |
| Copyright terms: Public domain | W3C validator |