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Theorem inrot 3201
 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 3200 . 2 ((𝐴𝐵) ∩ 𝐶) = ((𝐶𝐵) ∩ 𝐴)
2 in32 3198 . 2 ((𝐶𝐵) ∩ 𝐴) = ((𝐶𝐴) ∩ 𝐵)
31, 2eqtri 2105 1 ((𝐴𝐵) ∩ 𝐶) = ((𝐶𝐴) ∩ 𝐵)
 Colors of variables: wff set class Syntax hints:   = wceq 1287   ∩ cin 2985 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067 This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2616  df-in 2992 This theorem is referenced by: (None)
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