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Theorem inrot 4225
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 4224 . 2 ((𝐴𝐵) ∩ 𝐶) = ((𝐶𝐵) ∩ 𝐴)
2 in32 4222 . 2 ((𝐶𝐵) ∩ 𝐴) = ((𝐶𝐴) ∩ 𝐵)
31, 2eqtri 2756 1 ((𝐴𝐵) ∩ 𝐶) = ((𝐶𝐴) ∩ 𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1534  cin 3946
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3430  df-v 3473  df-in 3954
This theorem is referenced by: (None)
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