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Metamath Proof Explorer

Theorem nne

Description: Negation of inequality. (Contributed by NM, 9-Jun-2006)

Ref Expression
Assertion nne ⊢ ¬ A ≠ B ↔ A = B

Proof

Step Hyp Ref Expression
1 df-ne ⊢ A ≠ B ↔ ¬ A = B
2 1 con2bii ⊢ A = B ↔ ¬ A ≠ B
3 2 bicomi ⊢ ¬ A ≠ B ↔ A = B