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Metamath Proof Explorer

Theorem recoscld

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

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

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