Theorem sincld

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

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

Proof

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