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 ∈ ℂ → ( cos ‘ 𝐴 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		cosf	⊢ cos : ℂ ⟶ ℂ
2	1	ffvelcdmi	⊢ ( 𝐴 ∈ ℂ → ( cos ‘ 𝐴 ) ∈ ℂ )