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Theorem ne3anior 2602
Description: A De Morgan's law for inequality. (Contributed by NM, 30-Sep-2013.)
Assertion
Ref Expression
ne3anior ((AB CD EF) ↔ ¬ (A = B C = D E = F))

Proof of Theorem ne3anior
StepHypRef Expression
1 3anor 948 . 2 ((AB CD EF) ↔ ¬ (¬ AB ¬ CD ¬ EF))
2 nne 2520 . . 3 ABA = B)
3 nne 2520 . . 3 CDC = D)
4 nne 2520 . . 3 EFE = F)
52, 3, 43orbi123i 1141 . 2 ((¬ AB ¬ CD ¬ EF) ↔ (A = B C = D E = F))
61, 5xchbinx 301 1 ((AB CD EF) ↔ ¬ (A = B C = D E = F))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176   w3o 933   w3a 934   = wceq 1642  wne 2516
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-ne 2518
This theorem is referenced by: (None)
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