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Theorem inrot 3683
Description: Rotate the intersection of 3 classes. (Contributed by NM, 27-Aug-2012.)
Assertion
Ref Expression
inrot  |-  ( ( A  i^i  B )  i^i  C )  =  ( ( C  i^i  A )  i^i  B )

Proof of Theorem inrot
StepHypRef Expression
1 in31 3682 . 2  |-  ( ( A  i^i  B )  i^i  C )  =  ( ( C  i^i  B )  i^i  A )
2 in32 3680 . 2  |-  ( ( C  i^i  B )  i^i  A )  =  ( ( C  i^i  A )  i^i  B )
31, 2eqtri 2458 1  |-  ( ( A  i^i  B )  i^i  C )  =  ( ( C  i^i  A )  i^i  B )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437    i^i cin 3441
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 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-v 3089  df-in 3449
This theorem is referenced by: (None)
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