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Theorem undm 3427
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 3422 1  |-  ( _V 
\  ( A  u.  B ) )  =  ( ( _V  \  A )  i^i  ( _V  \  B ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1628   _Vcvv 2789    \ cdif 3150    u. cun 3151    i^i cin 3152
This theorem is referenced by:  difun1  3429
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549  ax-17 1608  ax-9 1641  ax-8 1648  ax-6 1707  ax-7 1712  ax-11 1719  ax-12 1869  ax-ext 2265
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1534  df-nf 1537  df-sb 1636  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ral 2549  df-rab 2553  df-v 2791  df-dif 3156  df-un 3158  df-in 3160
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