Theorem rpefcld

Description: The exponential of a real number is a positive real. (Contributed by Mario Carneiro, 29-May-2016)

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

Proof

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