Metamath Proof Explorer


Theorem renegi

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

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

Proof

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