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Theorem nelir 2803
Description: Inference associated with df-nel 2665. (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
StepHypRef Expression
1 nelir.1 . 2  |-  -.  A  e.  B
2 df-nel 2665 . 2  |-  ( A  e/  B  <->  -.  A  e.  B )
31, 2mpbir 209 1  |-  A  e/  B
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    e. wcel 1767    e/ wnel 2663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-nel 2665
This theorem is referenced by:  ru  3330  snnex  6584  ruv  8023  ruALT  8024  cardprc  8357  pnfnre  9631  mnfnre  9632  eirr  13795  sqrt2irr  13839  zfbas  20132  aaliou3  22481  bj-0nel1  33590  bj-1nel0  33591  bj-0nelsngl  33610
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