Theorem neli 2433

Description: Inference associated with df-nel 2432. (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 2432	. 2 |- ( A e/ B <-> -. A e. B )
3	1, 2	mpbi 144	1 |- -. A e. B

Syntax hints:   -. wn 3   e. wcel 2136   e/ wnel 2431

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 2432

This theorem is referenced by:  renepnf  7946  renemnf  7947  nn0nepnf  9185  xrltnr  9715  pnfnlt  9723  nltmnf  9724  inftonninf  10376  pcgcd1  12259  pc2dvds  12261  topnex  12726