Metamath Proof Explorer


Definition df-nel

Description: Define negated membership. (Contributed by NM, 7-Aug-1994)

Ref Expression
Assertion df-nel
|- ( A e/ B <-> -. A e. B )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA
 |-  A
1 cB
 |-  B
2 0 1 wnel
 |-  A e/ B
3 0 1 wcel
 |-  A e. B
4 3 wn
 |-  -. A e. B
5 2 4 wb
 |-  ( A e/ B <-> -. A e. B )