Theorem divcan2i

Description: A cancellation law for division. (Contributed by NM, 9-Feb-1995)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
	divcl.3	|- B =/= 0
Assertion	divcan2i	|- ( B x. ( A / B ) ) = A

Proof

Step	Hyp	Ref	Expression
1		divclz.1	|- A e. CC
2		divclz.2	|- B e. CC
3		divcl.3	|- B =/= 0
4	1 2	divcan2zi	|- ( B =/= 0 -> ( B x. ( A / B ) ) = A )
5	3 4	ax-mp	|- ( B x. ( A / B ) ) = A