Theorem cjdivd

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

	Ref	Expression
Hypotheses	recld.1	|- ( ph -> A e. CC )
	readdd.2	|- ( ph -> B e. CC )
	cjdivd.2	|- ( ph -> B =/= 0 )
Assertion	cjdivd	|- ( ph -> ( * ` ( A / B ) ) = ( ( * ` A ) / ( * ` B ) ) )

Proof

Step	Hyp	Ref	Expression
1		recld.1	|- ( ph -> A e. CC )
2		readdd.2	|- ( ph -> B e. CC )
3		cjdivd.2	|- ( ph -> B =/= 0 )
4		cjdiv	|- ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> ( * ` ( A / B ) ) = ( ( * ` A ) / ( * ` B ) ) )
5	1 2 3 4	syl3anc	|- ( ph -> ( * ` ( A / B ) ) = ( ( * ` A ) / ( * ` B ) ) )