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Theorem neli 2380
Description: Inference associated with df-nel 2379. (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 2379 . 2 (𝐴𝐵 ↔ ¬ 𝐴𝐵)
31, 2mpbi 144 1 ¬ 𝐴𝐵
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wcel 1463  wnel 2378
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116  df-nel 2379
This theorem is referenced by:  renepnf  7777  renemnf  7778  nn0nepnf  8999  xrltnr  9506  pnfnlt  9513  nltmnf  9514  inftonninf  10154  topnex  12150
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