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| Mirrors > Home > MPE Home > Th. List > necomd | Structured version Visualization version GIF version | ||
| Description: Deduction from commutative law for inequality. (Contributed by NM, 12-Feb-2008.) |
| Ref | Expression |
|---|---|
| necomd.1 | ⊢ (𝜑 → 𝐴 ≠ 𝐵) |
| Ref | Expression |
|---|---|
| necomd | ⊢ (𝜑 → 𝐵 ≠ 𝐴) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | necomd.1 | . 2 ⊢ (𝜑 → 𝐴 ≠ 𝐵) | |
| 2 | necom 2994 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ 𝐵 ≠ 𝐴) | |
| 3 | 1, 2 | sylib 218 | 1 ⊢ (𝜑 → 𝐵 ≠ 𝐴) |
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