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Theorem indm 3845
 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 3840 1 (V ∖ (𝐴𝐵)) = ((V ∖ 𝐴) ∪ (V ∖ 𝐵))
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  Vcvv 3173   ∖ cdif 3537   ∪ cun 3538   ∩ cin 3539 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547 This theorem is referenced by:  difdifdir  4008
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