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Theorem nesym 2294
Description: Characterization of inequality in terms of reversed equality (see bicom 138). (Contributed by BJ, 7-Jul-2018.)
Assertion
Ref Expression
nesym (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)

Proof of Theorem nesym
StepHypRef Expression
1 eqcom 2085 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
21necon3abii 2285 1 (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 103   = wceq 1285  wne 2249
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-ne 2250
This theorem is referenced by:  nesymi  2295  nesymir  2296  0neqopab  5629  fzdifsuc  9388  isprm3  10880
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