Theorem nelir 2406

Description: Inference associated with df-nel 2404. (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 2404	. 2 |- ( A e/ B <-> -. A e. B )
3	1, 2	mpbir 145	1 |- A e/ B

Syntax hints:   -. wn 3   e. wcel 1480   e/ wnel 2403

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 2404

This theorem is referenced by:  prneli  3552  snnex  4369  ruv  4465  pnfnre  7814  mnfnre  7815  eirr  11492  sqrt2irr  11847  topnex  12265