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Theorem indm 3560
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 3555 1  |-  ( _V 
\  ( A  i^i  B ) )  =  ( ( _V  \  A
)  u.  ( _V 
\  B ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1649   _Vcvv 2916    \ cdif 3277    u. cun 3278    i^i cin 3279
This theorem is referenced by:  difdifdir  3675
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287
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