Theorem divdiv32i

Description: Swap denominators in a division. (Contributed by NM, 15-Sep-1999)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
	divmulz.3	|- C e. CC
	divmul.4	|- B =/= 0
	divdiv23.5	|- C =/= 0
Assertion	divdiv32i	|- ( ( A / B ) / C ) = ( ( A / C ) / 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		divmul.4	|- B =/= 0
5		divdiv23.5	|- C =/= 0
6	1 2 3	divdiv23zi	|- ( ( B =/= 0 /\ C =/= 0 ) -> ( ( A / B ) / C ) = ( ( A / C ) / B ) )
7	4 5 6	mp2an	|- ( ( A / B ) / C ) = ( ( A / C ) / B )