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Mirrors > Home > MPE Home > Th. List > df-ne | Structured version Visualization version GIF version |
Description: Define inequality. (Contributed by NM, 26-May-1993.) |
Ref | Expression |
---|---|
df-ne | ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cB | . . 3 class 𝐵 | |
3 | 1, 2 | wne 2945 | . 2 wff 𝐴 ≠ 𝐵 |
4 | 1, 2 | wceq 1542 | . . 3 wff 𝐴 = 𝐵 |
5 | 4 | wn 3 | . 2 wff ¬ 𝐴 = 𝐵 |
6 | 3, 5 | wb 205 | 1 wff (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵) |
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