Theorem nelir 2445

Description: Inference associated with df-nel 2443. (Contributed by BJ, 7-Jul-2018.)

Hypothesis

Ref	Expression
nelir.1	|- -. A e. B

Assertion

Ref	Expression
nelir	|- A e/ B

Proof of Theorem nelir

Step	Hyp	Ref	Expression
1		nelir.1	. 2 |- -. A e. B
2		df-nel 2443	. 2 |- ( A e/ B <-> -. A e. B )
3	1, 2	mpbir 146	1 |- A e/ B

Syntax hints:   -. wn 3   e. wcel 2148   e/ wnel 2442

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-nel 2443

This theorem is referenced by:  prneli  3619  snnex  4450  ruv  4551  pnfnre  8001  mnfnre  8002  eirr  11788  sqrt2irr  12164  topnex  13671