Metamath Proof Explorer

Theorem cjcld

Description: Closure law for complex conjugate. (Contributed by Mario Carneiro, 29-May-2016)

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

Proof

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