Theorem cjsubd

Description: Complex conjugate distributes over subtraction. (Contributed by Thierry Arnoux, 1-Jul-2025)

	Ref	Expression
Hypotheses	cjsubd.1	|- ( ph -> A e. CC )
	cjsubd.2	|- ( ph -> B e. CC )
Assertion	cjsubd	|- ( ph -> ( * ` ( A - B ) ) = ( ( * ` A ) - ( * ` B ) ) )

Proof

Step	Hyp	Ref	Expression
1		cjsubd.1	|- ( ph -> A e. CC )
2		cjsubd.2	|- ( ph -> B e. CC )
3		cjsub	|- ( ( A e. CC /\ B e. CC ) -> ( * ` ( A - B ) ) = ( ( * ` A ) - ( * ` B ) ) )
4	1 2 3	syl2anc	|- ( ph -> ( * ` ( A - B ) ) = ( ( * ` A ) - ( * ` B ) ) )