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| Mirrors > Home > MPE Home > Th. List > neneqd | Structured version Visualization version GIF version | ||
| Description: Deduction eliminating inequality definition. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
| Ref | Expression |
|---|---|
| neneqd.1 | ⊢ (𝜑 → 𝐴 ≠ 𝐵) |
| Ref | Expression |
|---|---|
| neneqd | ⊢ (𝜑 → ¬ 𝐴 = 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | neneqd.1 | . 2 ⊢ (𝜑 → 𝐴 ≠ 𝐵) | |
| 2 | df-ne 2941 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵) | |
| 3 | 1, 2 | sylib 218 | 1 ⊢ (𝜑 → ¬ 𝐴 = 𝐵) |
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