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Theorem inrot 3470
 Description: Rotate the intersection of 3 classes. (Contributed by NM, 27-Aug-2012.)
Assertion
Ref Expression
inrot ((AB) ∩ C) = ((CA) ∩ B)

Proof of Theorem inrot
StepHypRef Expression
1 in31 3469 . 2 ((AB) ∩ C) = ((CB) ∩ A)
2 in32 3467 . 2 ((CB) ∩ A) = ((CA) ∩ B)
31, 2eqtri 2373 1 ((AB) ∩ C) = ((CA) ∩ B)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∩ cin 3208 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213 This theorem is referenced by: (None)
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