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Theorem neli 2444
Description: Inference associated with df-nel 2443. (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 2443 . 2  |-  ( A  e/  B  <->  -.  A  e.  B )
31, 2mpbi 145 1  |-  -.  A  e.  B
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 2148    e/ wnel 2442
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106
This theorem depends on definitions:  df-bi 117  df-nel 2443
This theorem is referenced by:  renepnf  7982  renemnf  7983  nn0nepnf  9223  xrltnr  9753  pnfnlt  9761  nltmnf  9762  inftonninf  10414  pcgcd1  12297  pc2dvds  12299  topnex  13219
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