Theorem cjsubd

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

	Ref	Expression
Hypotheses	cjsubd.1	$$⊢\phi \to A\in ℂ$$
	cjsubd.2	$$⊢\phi \to B\in ℂ$$
Assertion	cjsubd	$$⊢\phi \to \overline{A-B}=\bar{A}-\bar{B}$$

Proof

Step	Hyp	Ref	Expression
1		cjsubd.1	$$⊢\phi \to A\in ℂ$$
2		cjsubd.2	$$⊢\phi \to B\in ℂ$$
3		cjsub	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to \overline{A-B}=\bar{A}-\bar{B}$$
4	1 2 3	syl2anc	$$⊢\phi \to \overline{A-B}=\bar{A}-\bar{B}$$