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Theorem indm 4035
Description: De Morgan's law for intersection. Theorem 5.2(13') of [Stoll] p. 19. (Contributed by NM, 18-Aug-2004.)
Assertion
Ref Expression
indm (V ∖ (𝐴𝐵)) = ((V ∖ 𝐴) ∪ (V ∖ 𝐵))

Proof of Theorem indm
StepHypRef Expression
1 difindi 4030 1 (V ∖ (𝐴𝐵)) = ((V ∖ 𝐴) ∪ (V ∖ 𝐵))
Colors of variables: wff setvar class
Syntax hints:   = wceq 1631  Vcvv 3351  cdif 3720  cun 3721  cin 3722
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ral 3066  df-rab 3070  df-v 3353  df-dif 3726  df-un 3728  df-in 3730
This theorem is referenced by:  difdifdir  4199
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