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Theorem inrot 3261
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 3260 . 2 ((𝐴𝐵) ∩ 𝐶) = ((𝐶𝐵) ∩ 𝐴)
2 in32 3258 . 2 ((𝐶𝐵) ∩ 𝐴) = ((𝐶𝐴) ∩ 𝐵)
31, 2eqtri 2138 1 ((𝐴𝐵) ∩ 𝐶) = ((𝐶𝐴) ∩ 𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1316  cin 3040
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-in 3047
This theorem is referenced by: (None)
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