Theorem divcan3zi

Description: A cancellation law for division. (Eliminates a hypothesis of divcan3i with the weak deduction theorem.) (Contributed by NM, 3-Feb-2004)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
Assertion	divcan3zi	|- ( B =/= 0 -> ( ( B x. A ) / B ) = A )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	|- A e. CC
2		divclz.2	|- B e. CC
3		divcan3	|- ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> ( ( B x. A ) / B ) = A )
4	1 2 3	mp3an12	|- ( B =/= 0 -> ( ( B x. A ) / B ) = A )