Metamath Proof Explorer


Definition df-ne

Description: Define inequality. (Contributed by NM, 26-May-1993)

Ref Expression
Assertion df-ne ⊢ A ≠ B ↔ ¬ A = B

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA class A
1 cB class B
2 0 1 wne wff A ≠ B
3 0 1 wceq wff A = B
4 3 wn wff ¬ A = B
5 2 4 wb wff A ≠ B ↔ ¬ A = B