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Theorem indifcom 3578
Description: Commutation law for intersection and difference. (Contributed by Scott Fenton, 18-Feb-2013.)
Assertion
Ref Expression
indifcom  |-  ( A  i^i  ( B  \  C ) )  =  ( B  i^i  ( A  \  C ) )

Proof of Theorem indifcom
StepHypRef Expression
1 incom 3525 . . 3  |-  ( A  i^i  B )  =  ( B  i^i  A
)
21difeq1i 3453 . 2  |-  ( ( A  i^i  B ) 
\  C )  =  ( ( B  i^i  A )  \  C )
3 indif2 3576 . 2  |-  ( A  i^i  ( B  \  C ) )  =  ( ( A  i^i  B )  \  C )
4 indif2 3576 . 2  |-  ( B  i^i  ( A  \  C ) )  =  ( ( B  i^i  A )  \  C )
52, 3, 43eqtr4i 2465 1  |-  ( A  i^i  ( B  \  C ) )  =  ( B  i^i  ( A  \  C ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1652    \ cdif 3309    i^i cin 3311
This theorem is referenced by:  dfsup3OLD  7441  ufprim  17933  cmmbl  19421  unmbl  19424  volinun  19432  limciun  19773
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 2416
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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315  df-in 3319
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