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Theorem indm 3919
 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 3914 1 (V ∖ (𝐴𝐵)) = ((V ∖ 𝐴) ∪ (V ∖ 𝐵))
 Colors of variables: wff setvar class Syntax hints:   = wceq 1523  Vcvv 3231   ∖ cdif 3604   ∪ cun 3605   ∩ cin 3606 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614 This theorem is referenced by:  difdifdir  4089
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