Theorem inrot

Description: Rotate the intersection of 3 classes. (Contributed by NM, 27-Aug-2012)

	Ref	Expression
Assertion	inrot	$$⊢\left(A\cap B\right)\cap C=\left(C\cap A\right)\cap B$$

Proof

Step	Hyp	Ref	Expression
1		in31	$$⊢\left(A\cap B\right)\cap C=\left(C\cap B\right)\cap A$$
2		in32	$$⊢\left(C\cap B\right)\cap A=\left(C\cap A\right)\cap B$$
3	1 2	eqtri	$$⊢\left(A\cap B\right)\cap C=\left(C\cap A\right)\cap B$$