Theorem imcjd

Description: Imaginary part of a complex conjugate. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	recld.1	$$⊢\phi \to A\in ℂ$$
Assertion	imcjd	$$⊢\phi \to \Im \left(\bar{A}\right)=-\Im \left(A\right)$$

Proof

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