Theorem absdivzi

Description: Absolute value distributes over division. (Contributed by NM, 26-Mar-2005)

	Ref	Expression
Hypotheses	absvalsqi.1	|- A e. CC
	abssub.2	|- B e. CC
Assertion	absdivzi	|- ( B =/= 0 -> ( abs ` ( A / B ) ) = ( ( abs ` A ) / ( abs ` B ) ) )

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	|- A e. CC
2		abssub.2	|- B e. CC
3		absdiv	|- ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> ( abs ` ( A / B ) ) = ( ( abs ` A ) / ( abs ` B ) ) )
4	1 2 3	mp3an12	|- ( B =/= 0 -> ( abs ` ( A / B ) ) = ( ( abs ` A ) / ( abs ` B ) ) )