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 e. CC
	mvlrmuli.2	|- B e. CC
	mvlrmuli.3	|- B =/= 0
	mvlrmuli.4	|- ( A x. B ) = C
Assertion	mvlrmuli	|- A = ( C / B )

Proof

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