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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
StepHypRef Expression
1 nelir.1 . 2  |-  -.  A  e.  B
2 df-nel 2207 . 2  |-  ( A  e/  B  <->  -.  A  e.  B )
31, 2mpbir 134 1  |-  A  e/  B
Colors of variables: wff set class
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
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