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
 |-  A
1 cB
 |-  B
2 0 1 wne
 |-  A =/= B
3 0 1 wceq
 |-  A = B
4 3 wn
 |-  -. A = B
5 2 4 wb
 |-  ( A =/= B <-> -. A = B )