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	$$⊢A\in ℂ$$
	mvllmuli.2	$$⊢B\in ℂ$$
	mvllmuli.3	$$⊢A\ne 0$$
	mvllmuli.4	$$⊢AB=C$$
Assertion	mvllmuli	$$⊢B=\frac{C}{A}$$

Proof

Step	Hyp	Ref	Expression
1		mvllmuli.1	$$⊢A\in ℂ$$
2		mvllmuli.2	$$⊢B\in ℂ$$
3		mvllmuli.3	$$⊢A\ne 0$$
4		mvllmuli.4	$$⊢AB=C$$
5	2 1 3	divcan4i	$$⊢\frac{BA}{A}=B$$
6	1 2 4	mulcomli	$$⊢BA=C$$
7	6	oveq1i	$$⊢\frac{BA}{A}=\frac{C}{A}$$
8	5 7	eqtr3i	$$⊢B=\frac{C}{A}$$