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Theorem indifcom 3529
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 3476 . . 3  |-  ( A  i^i  B )  =  ( B  i^i  A
)
21difeq1i 3404 . 2  |-  ( ( A  i^i  B ) 
\  C )  =  ( ( B  i^i  A )  \  C )
3 indif2 3527 . 2  |-  ( A  i^i  ( B  \  C ) )  =  ( ( A  i^i  B )  \  C )
4 indif2 3527 . 2  |-  ( B  i^i  ( A  \  C ) )  =  ( ( B  i^i  A )  \  C )
52, 3, 43eqtr4i 2417 1  |-  ( A  i^i  ( B  \  C ) )  =  ( B  i^i  ( A  \  C ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1649    \ cdif 3260    i^i cin 3262
This theorem is referenced by:  dfsup3OLD  7384  ufprim  17862  cmmbl  19296  unmbl  19299  volinun  19307  limciun  19648
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 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
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 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ral 2654  df-rab 2658  df-v 2901  df-dif 3266  df-in 3270
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