Theorem coscld

Description: Closure of the cosine function. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	sincld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	coscld	⊢ ( 𝜑 → ( cos ‘ 𝐴 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		sincld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		coscl	⊢ ( 𝐴 ∈ ℂ → ( cos ‘ 𝐴 ) ∈ ℂ )
3	1 2	syl	⊢ ( 𝜑 → ( cos ‘ 𝐴 ) ∈ ℂ )