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Theorem indm 3732
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 3727 1  |-  ( _V 
\  ( A  i^i  B ) )  =  ( ( _V  \  A
)  u.  ( _V 
\  B ) )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437   _Vcvv 3081    \ cdif 3433    u. cun 3434    i^i cin 3435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ral 2780  df-rab 2784  df-v 3083  df-dif 3439  df-un 3441  df-in 3443
This theorem is referenced by:  difdifdir  3883
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