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Theorem nesym 2392
Description: Characterization of inequality in terms of reversed equality (see bicom 140). (Contributed by BJ, 7-Jul-2018.)
Assertion
Ref Expression
nesym (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)

Proof of Theorem nesym
StepHypRef Expression
1 eqcom 2179 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
21necon3abii 2383 1 (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 105   = wceq 1353  wne 2347
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-5 1447  ax-gen 1449  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-ne 2348
This theorem is referenced by:  nesymi  2393  nesymir  2394  0neqopab  5916  fzdifsuc  10075  isprm3  12109
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