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Theorem nelir 2360
Description: Inference associated with df-nel 2358. (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 2358 . 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 1445    e/ wnel 2357
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-nel 2358
This theorem is referenced by:  prneli  3491  snnex  4298  ruv  4394  pnfnre  7626  mnfnre  7627  eirr  11215  sqrt2irr  11568  topnex  11938
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