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Metamath Proof Explorer

Theorem recoshcl

Description: The hyperbolic cosine of a real number is real. (Contributed by Mario Carneiro, 4-Apr-2015)

		Ref	Expression
	Assertion	recoshcl	$⊢ A \in ℝ \to \cos i A \in ℝ$

Step	Hyp	Ref	Expression
1		rpcoshcl	$⊢ A \in ℝ \to \cos i A \in ℝ^{+}$
2	1	rpred	$⊢ A \in ℝ \to \cos i A \in ℝ$