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Theorem undm 3877
Description: De Morgan's law for union. Theorem 5.2(13) of [Stoll] p. 19. (Contributed by NM, 18-Aug-2004.)
Assertion
Ref Expression
undm (V ∖ (𝐴𝐵)) = ((V ∖ 𝐴) ∩ (V ∖ 𝐵))

Proof of Theorem undm
StepHypRef Expression
1 difundi 3871 1 (V ∖ (𝐴𝐵)) = ((V ∖ 𝐴) ∩ (V ∖ 𝐵))
Colors of variables: wff setvar class
Syntax hints:   = wceq 1481  Vcvv 3195  cdif 3564  cun 3565  cin 3566
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-ral 2914  df-rab 2918  df-v 3197  df-dif 3570  df-un 3572  df-in 3574
This theorem is referenced by:  difun1  3879
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