Metamath Proof Explorer


Theorem neli

Description: Inference associated with df-nel . (Contributed by BJ, 7-Jul-2018)

Ref Expression
Hypothesis neli.1
|- A e/ B
Assertion neli
|- -. A e. B

Proof

Step Hyp Ref Expression
1 neli.1
 |-  A e/ B
2 df-nel
 |-  ( A e/ B <-> -. A e. B )
3 1 2 mpbi
 |-  -. A e. B