Metamath Proof Explorer


Theorem addcjd

Description: A number plus its conjugate is twice its real part. Compare Proposition 10-3.4(h) of Gleason p. 133. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis recld.1
|- ( ph -> A e. CC )
Assertion addcjd
|- ( ph -> ( A + ( * ` A ) ) = ( 2 x. ( Re ` A ) ) )

Proof

Step Hyp Ref Expression
1 recld.1
 |-  ( ph -> A e. CC )
2 addcj
 |-  ( A e. CC -> ( A + ( * ` A ) ) = ( 2 x. ( Re ` A ) ) )
3 1 2 syl
 |-  ( ph -> ( A + ( * ` A ) ) = ( 2 x. ( Re ` A ) ) )