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Metamath Proof Explorer

Theorem neeq2

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

Proof

Step Hyp Ref Expression
1 id ⊢ A = B → A = B
2 1 neeq2d ⊢ A = B → C ≠ A ↔ C ≠ B