Metamath Proof Explorer

Theorem recji

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

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

Proof

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