Theorem rpefcl

Description: The exponential of a real number is a positive real. (Contributed by Mario Carneiro, 10-Nov-2013)

	Ref	Expression
Assertion	rpefcl	⊢ ( 𝐴 ∈ ℝ → ( exp ‘ 𝐴 ) ∈ ℝ+ )

Proof

Step	Hyp	Ref	Expression
1		reefcl	⊢ ( 𝐴 ∈ ℝ → ( exp ‘ 𝐴 ) ∈ ℝ )
2		efgt0	⊢ ( 𝐴 ∈ ℝ → 0 < ( exp ‘ 𝐴 ) )
3	1 2	elrpd	⊢ ( 𝐴 ∈ ℝ → ( exp ‘ 𝐴 ) ∈ ℝ+ )