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Theorem undm 3333
Description: DeMorgan's law for union. Theorem 5.2(13) of [Stoll] p. 19. (Contributed by NM, 18-Aug-2004.)
Assertion
Ref Expression
undm  |-  ( _V 
\  ( A  u.  B ) )  =  ( ( _V  \  A )  i^i  ( _V  \  B ) )

Proof of Theorem undm
StepHypRef Expression
1 difundi 3328 1  |-  ( _V 
\  ( A  u.  B ) )  =  ( ( _V  \  A )  i^i  ( _V  \  B ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1619   _Vcvv 2727    \ cdif 3075    u. cun 3076    i^i cin 3077
This theorem is referenced by:  difun1  3335
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085
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