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Theorem nesym 2244
Description: Characterization of inequality in terms of reversed equality (see bicom 128). (Contributed by BJ, 7-Jul-2018.)
Assertion
Ref Expression
nesym (AB ↔ ¬ B = A)

Proof of Theorem nesym
StepHypRef Expression
1 eqcom 2039 . 2 (A = BB = A)
21necon3abii 2235 1 (AB ↔ ¬ B = A)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98   = wceq 1242  wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-ne 2203
This theorem is referenced by:  nesymi  2245  nesymir  2246  0neqopab  5492  fzdifsuc  8693
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