Theorem divcan1i

Description: A cancellation law for division. (Contributed by NM, 18-May-1999)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
	divcl.3	|- B =/= 0
Assertion	divcan1i	|- ( ( A / B ) x. 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 3	divcli	|- ( A / B ) e. CC
5	1 2 3	divcan2i	|- ( B x. ( A / B ) ) = A
6	2 4 5	mulcomli	|- ( ( A / B ) x. B ) = A