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Theorem nesym 2265
Description: Characterization of inequality in terms of reversed equality (see bicom 132). (Contributed by BJ, 7-Jul-2018.)
Assertion
Ref Expression
nesym (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)

Proof of Theorem nesym
StepHypRef Expression
1 eqcom 2058 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
21necon3abii 2256 1 (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 102   = wceq 1259  wne 2220
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-ne 2221
This theorem is referenced by:  nesymi  2266  nesymir  2267  0neqopab  5577  fzdifsuc  9044
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