Theorem mvllmuli

Description: Move the left term in a product on the LHS to the RHS, inference form. Uses divcan4i . (Contributed by David A. Wheeler, 11-Oct-2018)

	Ref	Expression
Hypotheses	mvllmuli.1	|- A e. CC
	mvllmuli.2	|- B e. CC
	mvllmuli.3	|- A =/= 0
	mvllmuli.4	|- ( A x. B ) = C
Assertion	mvllmuli	|- B = ( C / A )

Proof

Step	Hyp	Ref	Expression
1		mvllmuli.1	|- A e. CC
2		mvllmuli.2	|- B e. CC
3		mvllmuli.3	|- A =/= 0
4		mvllmuli.4	|- ( A x. B ) = C
5	2 1 3	divcan4i	|- ( ( B x. A ) / A ) = B
6	1 2 4	mulcomli	|- ( B x. A ) = C
7	6	oveq1i	|- ( ( B x. A ) / A ) = ( C / A )
8	5 7	eqtr3i	|- B = ( C / A )