Description: Logical OR with an equality. (Contributed by NM, 29-Apr-2007)
Ref | Expression | ||
---|---|---|---|
Assertion | neor | ⊢ ( ( 𝐴 = 𝐵 ∨ 𝜓 ) ↔ ( 𝐴 ≠ 𝐵 → 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-or | ⊢ ( ( 𝐴 = 𝐵 ∨ 𝜓 ) ↔ ( ¬ 𝐴 = 𝐵 → 𝜓 ) ) | |
2 | df-ne | ⊢ ( 𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵 ) | |
3 | 2 | imbi1i | ⊢ ( ( 𝐴 ≠ 𝐵 → 𝜓 ) ↔ ( ¬ 𝐴 = 𝐵 → 𝜓 ) ) |
4 | 1 3 | bitr4i | ⊢ ( ( 𝐴 = 𝐵 ∨ 𝜓 ) ↔ ( 𝐴 ≠ 𝐵 → 𝜓 ) ) |