Theorem div23i

Description: A commutative/associative law for division. (Contributed by NM, 3-Sep-1999)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
	divmulz.3	|- C e. CC
	divass.4	|- C =/= 0
Assertion	div23i	|- ( ( A x. B ) / C ) = ( ( A / C ) x. B )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	|- A e. CC
2		divclz.2	|- B e. CC
3		divmulz.3	|- C e. CC
4		divass.4	|- C =/= 0
5	3 4	pm3.2i	|- ( C e. CC /\ C =/= 0 )
6		div23	|- ( ( A e. CC /\ B e. CC /\ ( C e. CC /\ C =/= 0 ) ) -> ( ( A x. B ) / C ) = ( ( A / C ) x. B ) )
7	1 2 5 6	mp3an	|- ( ( A x. B ) / C ) = ( ( A / C ) x. B )