Theorem in31

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

	Ref	Expression
Assertion	in31	$$⊢\left(A\cap B\right)\cap C=\left(C\cap B\right)\cap A$$

Proof

Step	Hyp	Ref	Expression
1		in12	$$⊢C\cap \left(A\cap B\right)=A\cap \left(C\cap B\right)$$
2		incom	$$⊢\left(A\cap B\right)\cap C=C\cap \left(A\cap B\right)$$
3		incom	$$⊢\left(C\cap B\right)\cap A=A\cap \left(C\cap B\right)$$
4	1 2 3	3eqtr4i	$$⊢\left(A\cap B\right)\cap C=\left(C\cap B\right)\cap A$$