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Theorem indifcom 3728
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 3676 . . 3  |-  ( A  i^i  B )  =  ( B  i^i  A
)
21difeq1i 3603 . 2  |-  ( ( A  i^i  B ) 
\  C )  =  ( ( B  i^i  A )  \  C )
3 indif2 3726 . 2  |-  ( A  i^i  ( B  \  C ) )  =  ( ( A  i^i  B )  \  C )
4 indif2 3726 . 2  |-  ( B  i^i  ( A  \  C ) )  =  ( ( B  i^i  A )  \  C )
52, 3, 43eqtr4i 2482 1  |-  ( A  i^i  ( B  \  C ) )  =  ( B  i^i  ( A  \  C ) )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1383    \ cdif 3458    i^i cin 3460
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ral 2798  df-rab 2802  df-v 3097  df-dif 3464  df-in 3468
This theorem is referenced by:  dfsup3OLD  7906  ufprim  20283  cmmbl  21818  unmbl  21821  volinun  21829  limciun  22171
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