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Theorem in13 3284
Description: A rearrangement of intersection. (Contributed by NM, 27-Aug-2012.)
Assertion
Ref Expression
in13  |-  ( A  i^i  ( B  i^i  C ) )  =  ( C  i^i  ( B  i^i  A ) )

Proof of Theorem in13
StepHypRef Expression
1 in32 3283 . 2  |-  ( ( B  i^i  C )  i^i  A )  =  ( ( B  i^i  A )  i^i  C )
2 incom 3263 . 2  |-  ( A  i^i  ( B  i^i  C ) )  =  ( ( B  i^i  C
)  i^i  A )
3 incom 3263 . 2  |-  ( C  i^i  ( B  i^i  A ) )  =  ( ( B  i^i  A
)  i^i  C )
41, 2, 33eqtr4i 2168 1  |-  ( A  i^i  ( B  i^i  C ) )  =  ( C  i^i  ( B  i^i  A ) )
Colors of variables: wff set class
Syntax hints:    = wceq 1331    i^i cin 3065
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-in 3072
This theorem is referenced by: (None)
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