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Theorem indifcom 3211
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 3157 . . 3  |-  ( A  i^i  B )  =  ( B  i^i  A
)
21difeq1i 3086 . 2  |-  ( ( A  i^i  B ) 
\  C )  =  ( ( B  i^i  A )  \  C )
3 indif2 3209 . 2  |-  ( A  i^i  ( B  \  C ) )  =  ( ( A  i^i  B )  \  C )
4 indif2 3209 . 2  |-  ( B  i^i  ( A  \  C ) )  =  ( ( B  i^i  A )  \  C )
52, 3, 43eqtr4i 2086 1  |-  ( A  i^i  ( B  \  C ) )  =  ( B  i^i  ( A  \  C ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1259    \ cdif 2942    i^i cin 2944
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rab 2332  df-v 2576  df-dif 2948  df-in 2952
This theorem is referenced by: (None)
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