Theorem mul32i

Description: Commutative/associative law that swaps the last two factors in a triple product. (Contributed by NM, 11-May-1999)

	Ref	Expression
Hypotheses	mul.1	|- A e. CC
	mul.2	|- B e. CC
	mul.3	|- C e. CC
Assertion	mul32i	|- ( ( A x. B ) x. C ) = ( ( A x. C ) x. B )

Proof

Step	Hyp	Ref	Expression
1		mul.1	|- A e. CC
2		mul.2	|- B e. CC
3		mul.3	|- C e. CC
4		mul32	|- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A x. B ) x. C ) = ( ( A x. C ) x. B ) )
5	1 2 3 4	mp3an	|- ( ( A x. B ) x. C ) = ( ( A x. C ) x. B )