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Theorem undm 3839
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 3833 1 (V ∖ (𝐴𝐵)) = ((V ∖ 𝐴) ∩ (V ∖ 𝐵))
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  Vcvv 3168  cdif 3532  cun 3533  cin 3534
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-11 2019  ax-12 2031  ax-13 2228  ax-ext 2585
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1866  df-clab 2592  df-cleq 2598  df-clel 2601  df-nfc 2735  df-ral 2896  df-rab 2900  df-v 3170  df-dif 3538  df-un 3540  df-in 3542
This theorem is referenced by:  difun1  3841
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