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	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	rpefcld	⊢ ( 𝜑 → ( exp ‘ 𝐴 ) ∈ ℝ+ )

Proof

Step	Hyp	Ref	Expression
1		rpefcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		rpefcl	⊢ ( 𝐴 ∈ ℝ → ( exp ‘ 𝐴 ) ∈ ℝ+ )
3	1 2	syl	⊢ ( 𝜑 → ( exp ‘ 𝐴 ) ∈ ℝ+ )