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Theorem indm 3429
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 
\  ( A  i^i  B ) )  =  ( ( _V  \  A
)  u.  ( _V 
\  B ) )

Proof of Theorem indm
StepHypRef Expression
1 difindi 3425 1  |-  ( _V 
\  ( A  i^i  B ) )  =  ( ( _V  \  A
)  u.  ( _V 
\  B ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1625   _Vcvv 2790    \ cdif 3151    u. cun 3152    i^i cin 3153
This theorem is referenced by:  difdifdir  3543
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-ral 2550  df-rab 2554  df-v 2792  df-dif 3157  df-un 3159  df-in 3161
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