| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > necomi | Structured version Visualization version GIF version | ||
| Description: Inference from commutative law for inequality. (Contributed by NM, 17-Oct-2012.) |
| Ref | Expression |
|---|---|
| necomi.1 | ⊢ 𝐴 ≠ 𝐵 |
| Ref | Expression |
|---|---|
| necomi | ⊢ 𝐵 ≠ 𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | necomi.1 | . 2 ⊢ 𝐴 ≠ 𝐵 | |
| 2 | necom 2994 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ 𝐵 ≠ 𝐴) | |
| 3 | 1, 2 | mpbi 230 | 1 ⊢ 𝐵 ≠ 𝐴 |
| Copyright terms: Public domain | W3C validator |