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Theorem indm 3503
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 3499 1  |-  ( _V 
\  ( A  i^i  B ) )  =  ( ( _V  \  A
)  u.  ( _V 
\  B ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1642   _Vcvv 2864    \ cdif 3225    u. cun 3226    i^i cin 3227
This theorem is referenced by:  difdifdir  3617
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ral 2624  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235
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