Metamath Proof Explorer


Theorem addcji

Description: A number plus its conjugate is twice its real part. Compare Proposition 10-3.4(h) of Gleason p. 133. (Contributed by NM, 2-Oct-1999)

Ref Expression
Hypothesis recl.1
|- A e. CC
Assertion addcji
|- ( A + ( * ` A ) ) = ( 2 x. ( Re ` A ) )

Proof

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