Metamath Proof Explorer

Theorem imcji

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

Ref Expression
Hypothesis recl.1 
|- A e. CC
Assertion imcji 
|- ( Im ` ( * ` A ) ) = -u ( Im ` A )

Proof

Step Hyp Ref Expression
1 recl.1 
 |-  A e. CC
2 imcj 
 |-  ( A e. CC -> ( Im ` ( * ` A ) ) = -u ( Im ` A ) )
3 1 2 ax-mp 
 |-  ( Im ` ( * ` A ) ) = -u ( Im ` A )