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Theorem neli 2348
Description: Inference associated with df-nel 2347. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
neli.1 𝐴𝐵
Assertion
Ref Expression
neli ¬ 𝐴𝐵

Proof of Theorem neli
StepHypRef Expression
1 neli.1 . 2 𝐴𝐵
2 df-nel 2347 . 2 (𝐴𝐵 ↔ ¬ 𝐴𝐵)
31, 2mpbi 143 1 ¬ 𝐴𝐵
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wcel 1436  wnel 2346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115  df-nel 2347
This theorem is referenced by:  renepnf  7482  renemnf  7483  nn0nepnf  8680  xrltnr  9185  pnfnlt  9192  nltmnf  9193  inftonninf  9778
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