Theorem mul4i

Description: Rearrangement of 4 factors. (Contributed by NM, 16-Feb-1995)

	Ref	Expression
Hypotheses	mul.1	|- A e. CC
	mul.2	|- B e. CC
	mul.3	|- C e. CC
	mul4.4	|- D e. CC
Assertion	mul4i	|- ( ( A x. B ) x. ( C x. D ) ) = ( ( A x. C ) x. ( B x. D ) )

Proof

Step	Hyp	Ref	Expression
1		mul.1	|- A e. CC
2		mul.2	|- B e. CC
3		mul.3	|- C e. CC
4		mul4.4	|- D e. CC
5		mul4	|- ( ( ( A e. CC /\ B e. CC ) /\ ( C e. CC /\ D e. CC ) ) -> ( ( A x. B ) x. ( C x. D ) ) = ( ( A x. C ) x. ( B x. D ) ) )
6	1 2 3 4 5	mp4an	|- ( ( A x. B ) x. ( C x. D ) ) = ( ( A x. C ) x. ( B x. D ) )