Theorem imcjd

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

	Ref	Expression
Hypothesis	recld.1	|- ( ph -> A e. CC )
Assertion	imcjd	|- ( ph -> ( Im ` ( * ` A ) ) = -u ( Im ` A ) )

Proof

Step	Hyp	Ref	Expression
1		recld.1	|- ( ph -> A e. CC )
2		imcj	|- ( A e. CC -> ( Im ` ( * ` A ) ) = -u ( Im ` A ) )
3	1 2	syl	|- ( ph -> ( Im ` ( * ` A ) ) = -u ( Im ` A ) )