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Theorem in31 3557
Description: A rearrangement of intersection. (Contributed by NM, 27-Aug-2012.)
Assertion
Ref Expression
in31  |-  ( ( A  i^i  B )  i^i  C )  =  ( ( C  i^i  B )  i^i  A )

Proof of Theorem in31
StepHypRef Expression
1 in12 3554 . 2  |-  ( C  i^i  ( A  i^i  B ) )  =  ( A  i^i  ( C  i^i  B ) )
2 incom 3535 . 2  |-  ( ( A  i^i  B )  i^i  C )  =  ( C  i^i  ( A  i^i  B ) )
3 incom 3535 . 2  |-  ( ( C  i^i  B )  i^i  A )  =  ( A  i^i  ( C  i^i  B ) )
41, 2, 33eqtr4i 2468 1  |-  ( ( A  i^i  B )  i^i  C )  =  ( ( C  i^i  B )  i^i  A )
Colors of variables: wff set class
Syntax hints:    = wceq 1653    i^i cin 3321
This theorem is referenced by:  inrot  3558
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-in 3329
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