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Theorem inrot 3811
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 3810 . 2 ((𝐴𝐵) ∩ 𝐶) = ((𝐶𝐵) ∩ 𝐴)
2 in32 3808 . 2 ((𝐶𝐵) ∩ 𝐴) = ((𝐶𝐴) ∩ 𝐵)
31, 2eqtri 2648 1 ((𝐴𝐵) ∩ 𝐶) = ((𝐶𝐴) ∩ 𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  cin 3559
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-9 2001  ax-10 2021  ax-11 2036  ax-12 2049  ax-13 2250  ax-ext 2606
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1883  df-clab 2613  df-cleq 2619  df-clel 2622  df-nfc 2756  df-v 3193  df-in 3567
This theorem is referenced by: (None)
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