Metamath Proof Explorer


Theorem imnegi

Description: Imaginary part of negative. (Contributed by NM, 2-Aug-1999)

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

Proof

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