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Theorem neli 2352
Description: Inference associated with df-nel 2351. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
neli.1  |-  A  e/  B
Assertion
Ref Expression
neli  |-  -.  A  e.  B

Proof of Theorem neli
StepHypRef Expression
1 neli.1 . 2  |-  A  e/  B
2 df-nel 2351 . 2  |-  ( A  e/  B  <->  -.  A  e.  B )
31, 2mpbi 143 1  |-  -.  A  e.  B
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1438    e/ wnel 2350
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 2351
This theorem is referenced by:  renepnf  7514  renemnf  7515  nn0nepnf  8714  xrltnr  9219  pnfnlt  9226  nltmnf  9227  inftonninf  9812
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