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Theorem inrot 3718
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 3717 . 2  |-  ( ( A  i^i  B )  i^i  C )  =  ( ( C  i^i  B )  i^i  A )
2 in32 3715 . 2  |-  ( ( C  i^i  B )  i^i  A )  =  ( ( C  i^i  A )  i^i  B )
31, 2eqtri 2496 1  |-  ( ( A  i^i  B )  i^i  C )  =  ( ( C  i^i  A )  i^i  B )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379    i^i cin 3480
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3120  df-in 3488
This theorem is referenced by: (None)
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