Theorem inrot 3471

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 3470	. 2 |- ((A i^i B) i^i C) = ((C i^i B) i^i A)
2		in32 3468	. 2 |- ((C i^i B) i^i A) = ((C i^i A) i^i B)
3	1, 2	eqtri 2373	1 |- ((A i^i B) i^i C) = ((C i^i A) i^i B)

Syntax hints:   = wceq 1642   i^i cin 3209

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214

This theorem is referenced by: (None)