Metamath Proof Explorer

Theorem coscl

Description: Closure of the cosine function with a complex argument. (Contributed by NM, 28-Apr-2005) (Revised by Mario Carneiro, 30-Apr-2014)

Ref Expression
Assertion coscl 
|- ( A e. CC -> ( cos ` A ) e. CC )

Proof

Step Hyp Ref Expression
1 cosf 
 |-  cos : CC --> CC
2 1 ffvelcdmi 
 |-  ( A e. CC -> ( cos ` A ) e. CC )