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Theorem nner 2207
Description: Negation of inequality. (Contributed by Jim Kingdon, 23-Dec-2018.)
Assertion
Ref Expression
nner (A = B → ¬ AB)

Proof of Theorem nner
StepHypRef Expression
1 df-ne 2203 . . 3 (AB ↔ ¬ A = B)
21biimpi 113 . 2 (AB → ¬ A = B)
32con2i 557 1 (A = B → ¬ AB)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1242  wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110  df-ne 2203
This theorem is referenced by:  nn0eln0  4284  funtpg  4893
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