Theorem neli 2403

Description: Inference associated with df-nel 2402. (Contributed by BJ, 7-Jul-2018.)

Hypothesis

Ref	Expression
neli.1	|- A e/ B

Assertion

Ref	Expression
neli	|- -. A e. B

Proof of Theorem neli

Step	Hyp	Ref	Expression
1		neli.1	. 2 |- A e/ B
2		df-nel 2402	. 2 |- ( A e/ B <-> -. A e. B )
3	1, 2	mpbi 144	1 |- -. A e. B

Syntax hints:   -. wn 3   e. wcel 1480   e/ wnel 2401

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105

This theorem depends on definitions:  df-bi 116  df-nel 2402

This theorem is referenced by:  renepnf  7806  renemnf  7807  nn0nepnf  9041  xrltnr  9559  pnfnlt  9566  nltmnf  9567  inftonninf  10207  topnex  12244