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Theorem nner 2312
Description: Negation of inequality. (Contributed by Jim Kingdon, 23-Dec-2018.)
Assertion
Ref Expression
nner  |-  ( A  =  B  ->  -.  A  =/=  B )

Proof of Theorem nner
StepHypRef Expression
1 df-ne 2309 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
21biimpi 119 . 2  |-  ( A  =/=  B  ->  -.  A  =  B )
32con2i 616 1  |-  ( A  =  B  ->  -.  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1331    =/= wne 2308
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in1 603  ax-in2 604
This theorem depends on definitions:  df-bi 116  df-ne 2309
This theorem is referenced by:  nn0eln0  4533  funtpg  5174  fin0  6779  hashnncl  10549
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