Description: Equality theorem for inequality. (Contributed by NM, 19-Nov-1994) (Proof shortened by Wolf Lammen, 18-Nov-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | neeq2 | ⊢ ( 𝐴 = 𝐵 → ( 𝐶 ≠ 𝐴 ↔ 𝐶 ≠ 𝐵 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id | ⊢ ( 𝐴 = 𝐵 → 𝐴 = 𝐵 ) | |
2 | 1 | neeq2d | ⊢ ( 𝐴 = 𝐵 → ( 𝐶 ≠ 𝐴 ↔ 𝐶 ≠ 𝐵 ) ) |