Theorem cjdivi

Description: Complex conjugate distributes over division. (Contributed by NM, 29-Apr-2005) (Revised by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypotheses	recl.1	|- A e. CC
	readdi.2	|- B e. CC
Assertion	cjdivi	|- ( B =/= 0 -> ( * ` ( A / B ) ) = ( ( * ` A ) / ( * ` B ) ) )

Proof

Step	Hyp	Ref	Expression
1		recl.1	|- A e. CC
2		readdi.2	|- B e. CC
3		cjdiv	|- ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> ( * ` ( A / B ) ) = ( ( * ` A ) / ( * ` B ) ) )
4	1 2 3	mp3an12	|- ( B =/= 0 -> ( * ` ( A / B ) ) = ( ( * ` A ) / ( * ` B ) ) )