Theorem reefcld

Description: The exponential function is real if its argument is real. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	reefcld.1	|- ( ph -> A e. RR )
Assertion	reefcld	|- ( ph -> ( exp ` A ) e. RR )

Proof

Step	Hyp	Ref	Expression
1		reefcld.1	|- ( ph -> A e. RR )
2		reefcl	|- ( A e. RR -> ( exp ` A ) e. RR )
3	1 2	syl	|- ( ph -> ( exp ` A ) e. RR )