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Theorem undm 3586
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 
\  ( A  u.  B ) )  =  ( ( _V  \  A )  i^i  ( _V  \  B ) )

Proof of Theorem undm
StepHypRef Expression
1 difundi 3580 1  |-  ( _V 
\  ( A  u.  B ) )  =  ( ( _V  \  A )  i^i  ( _V  \  B ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1652   _Vcvv 2943    \ cdif 3304    u. cun 3305    i^i cin 3306
This theorem is referenced by:  difun1  3588
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2411
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2417  df-cleq 2423  df-clel 2426  df-nfc 2555  df-ral 2697  df-rab 2701  df-v 2945  df-dif 3310  df-un 3312  df-in 3314
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