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Theorem nelir 2317
Description: Inference associated with df-nel 2315. (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 2315 . 2  |-  ( A  e/  B  <->  -.  A  e.  B )
31, 2mpbir 138 1  |-  A  e/  B
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1409    e/ wnel 2314
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-nel 2315
This theorem is referenced by:  snnex  4209  ruv  4302  pnfnre  7126  mnfnre  7127  sqrt2irr  10251
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