Theorem recoscld

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

	Ref	Expression
Hypothesis	resincld.1	|- ( ph -> A e. RR )
Assertion	recoscld	|- ( ph -> ( cos ` A ) e. RR )

Proof

Step	Hyp	Ref	Expression
1		resincld.1	|- ( ph -> A e. RR )
2		recoscl	|- ( A e. RR -> ( cos ` A ) e. RR )
3	1 2	syl	|- ( ph -> ( cos ` A ) e. RR )