Theorem inrot 3440

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

Step	Hyp	Ref	Expression
1		in31 3439	. 2 |- ( ( A i^i B ) i^i C ) = ( ( C i^i B ) i^i A )
2		in32 3437	. 2 |- ( ( C i^i B ) i^i A ) = ( ( C i^i A ) i^i B )
3	1, 2	eqtri 2255	1 |- ( ( A i^i B ) i^i C ) = ( ( C i^i A ) i^i B )

Syntax hints:   = wceq 1398   i^i cin 3213

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-v 2817  df-in 3220

This theorem is referenced by: (None)