Theorem in31

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

	Ref	Expression
Assertion	in31	|- ( ( A i^i B ) i^i C ) = ( ( C i^i B ) i^i A )

Proof

Step	Hyp	Ref	Expression
1		in12	|- ( C i^i ( A i^i B ) ) = ( A i^i ( C i^i B ) )
2		incom	|- ( ( A i^i B ) i^i C ) = ( C i^i ( A i^i B ) )
3		incom	|- ( ( C i^i B ) i^i A ) = ( A i^i ( C i^i B ) )
4	1 2 3	3eqtr4i	|- ( ( A i^i B ) i^i C ) = ( ( C i^i B ) i^i A )