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Theorem nner 2289
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 2286 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
21biimpi 119 . 2  |-  ( A  =/=  B  ->  -.  A  =  B )
32con2i 601 1  |-  ( A  =  B  ->  -.  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1316    =/= wne 2285
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in1 588  ax-in2 589
This theorem depends on definitions:  df-bi 116  df-ne 2286
This theorem is referenced by:  nn0eln0  4503  funtpg  5144  fin0  6747  hashnncl  10510
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