Theorem mvlrmuli

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

	Ref	Expression
Hypotheses	mvlrmuli.1	$$⊢A\in ℂ$$
	mvlrmuli.2	$$⊢B\in ℂ$$
	mvlrmuli.3	$$⊢B\ne 0$$
	mvlrmuli.4	$$⊢AB=C$$
Assertion	mvlrmuli	$$⊢A=\frac{C}{B}$$

Proof

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