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Theorem nner 2259
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 2256 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
21biimpi 118 . 2  |-  ( A  =/=  B  ->  -.  A  =  B )
32con2i 592 1  |-  ( A  =  B  ->  -.  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1289    =/= wne 2255
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-in1 579  ax-in2 580
This theorem depends on definitions:  df-bi 115  df-ne 2256
This theorem is referenced by:  nn0eln0  4433  funtpg  5065  fin0  6601  hashnncl  10204
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