Theorem in13

Description: A rearrangement of intersection. (Contributed by NM, 27-Aug-2012)

	Ref	Expression
Assertion	in13	$$⊢A\cap \left(B\cap C\right)=C\cap \left(B\cap A\right)$$

Proof

Step	Hyp	Ref	Expression
1		in32	$$⊢\left(B\cap C\right)\cap A=\left(B\cap A\right)\cap C$$
2		incom	$$⊢A\cap \left(B\cap C\right)=\left(B\cap C\right)\cap A$$
3		incom	$$⊢C\cap \left(B\cap A\right)=\left(B\cap A\right)\cap C$$
4	1 2 3	3eqtr4i	$$⊢A\cap \left(B\cap C\right)=C\cap \left(B\cap A\right)$$