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Theorem nesym 2224
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 2020 . 2 (A = BB = A)
21necon3abii 2215 1 (AB ↔ ¬ B = A)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98   = wceq 1226  wne 2182
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 532  ax-in2 533  ax-5 1312  ax-gen 1314  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-cleq 2011  df-ne 2184
This theorem is referenced by:  nesymi  2225  nesymir  2226  0neqopab  5469
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