Metamath Proof Explorer

Theorem cjnegd

Description: Complex conjugate of negative. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis recld.1 
|- ( ph -> A e. CC )
Assertion cjnegd 
|- ( ph -> ( * ` -u A ) = -u ( * ` A ) )

Proof

Step Hyp Ref Expression
1 recld.1 
 |-  ( ph -> A e. CC )
2 cjneg 
 |-  ( A e. CC -> ( * ` -u A ) = -u ( * ` A ) )
3 1 2 syl 
 |-  ( ph -> ( * ` -u A ) = -u ( * ` A ) )