Theorem recoscld

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

	Ref	Expression
Hypothesis	resincld.1	$$⊢\phi \to A\in ℝ$$
Assertion	recoscld	$$⊢\phi \to \cos A\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		resincld.1	$$⊢\phi \to A\in ℝ$$
2		recoscl	$$⊢A\in ℝ\to \cos A\in ℝ$$
3	1 2	syl	$$⊢\phi \to \cos A\in ℝ$$