Description: Define inequality. (Contributed by NM, 26-May-1993)
Ref | Expression | ||
---|---|---|---|
Assertion | df-ne | ⊢ ( 𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | cA | ⊢ 𝐴 | |
1 | cB | ⊢ 𝐵 | |
2 | 0 1 | wne | ⊢ 𝐴 ≠ 𝐵 |
3 | 0 1 | wceq | ⊢ 𝐴 = 𝐵 |
4 | 3 | wn | ⊢ ¬ 𝐴 = 𝐵 |
5 | 2 4 | wb | ⊢ ( 𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵 ) |