Theorem nelir 2360

Description: Inference associated with df-nel 2358. (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 2358	. 2 |- ( A e/ B <-> -. A e. B )
3	1, 2	mpbir 145	1 |- A e/ B

Syntax hints:   -. wn 3   e. wcel 1445   e/ wnel 2357

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

This theorem depends on definitions:  df-bi 116  df-nel 2358

This theorem is referenced by:  prneli  3491  snnex  4298  ruv  4394  pnfnre  7626  mnfnre  7627  eirr  11231  sqrt2irr  11584  topnex  11954