Theorem nelir 2300

Description: Inference associated with df-nel 2207. (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 2207	. 2 |- ( A e/ B <-> -. A e. B )
3	1, 2	mpbir 134	1 |- A e/ B

Syntax hints:   -. wn 3   e. wcel 1393   e/ wnel 2205

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-nel 2207

This theorem is referenced by:  snnex  4181  ruv  4274  pnfnre  7067  mnfnre  7068  sqrt2irr  9878