Theorem imcji

Description: Imaginary part of a complex conjugate. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypothesis	recl.1	$$⊢A\in ℂ$$
Assertion	imcji	$$⊢\Im \left(\bar{A}\right)=-\Im \left(A\right)$$

Proof

Step	Hyp	Ref	Expression
1		recl.1	$$⊢A\in ℂ$$
2		imcj	$$⊢A\in ℂ\to \Im \left(\bar{A}\right)=-\Im \left(A\right)$$
3	1 2	ax-mp	$$⊢\Im \left(\bar{A}\right)=-\Im \left(A\right)$$