Theorem nelir 2407

Description: Inference associated with df-nel 2405. (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 2405	. 2 |- ( A e/ B <-> -. A e. B )
3	1, 2	mpbir 145	1 |- A e/ B

Syntax hints:   -. wn 3   e. wcel 1481   e/ wnel 2404

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-nel 2405

This theorem is referenced by:  prneli  3557  snnex  4377  ruv  4473  pnfnre  7831  mnfnre  7832  eirr  11521  sqrt2irr  11876  topnex  12294