Theorem divcan1zi

Description: A cancellation law for division. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
Assertion	divcan1zi	|- ( B =/= 0 -> ( ( A / B ) x. B ) = A )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	|- A e. CC
2		divclz.2	|- B e. CC
3		divcan1	|- ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> ( ( A / B ) x. B ) = A )
4	1 2 3	mp3an12	|- ( B =/= 0 -> ( ( A / B ) x. B ) = A )