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Theorem nelir 2383
Description: Inference associated with df-nel 2381. (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 2381 . 2  |-  ( A  e/  B  <->  -.  A  e.  B )
31, 2mpbir 145 1  |-  A  e/  B
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1465    e/ wnel 2380
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 2381
This theorem is referenced by:  prneli  3522  snnex  4339  ruv  4435  pnfnre  7775  mnfnre  7776  eirr  11412  sqrt2irr  11767  topnex  12182
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