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Theorem nesym 2330
Description: Characterization of inequality in terms of reversed equality (see bicom 139). (Contributed by BJ, 7-Jul-2018.)
Assertion
Ref Expression
nesym (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)

Proof of Theorem nesym
StepHypRef Expression
1 eqcom 2119 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
21necon3abii 2321 1 (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 104   = wceq 1316  wne 2285
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-5 1408  ax-gen 1410  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-cleq 2110  df-ne 2286
This theorem is referenced by:  nesymi  2331  nesymir  2332  0neqopab  5784  fzdifsuc  9829  isprm3  11726
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