Theorem rpefcl

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

	Ref	Expression
Assertion	rpefcl	$$⊢A\in ℝ\to {\mathrm{e}}^A\in {ℝ}^{+}$$

Proof

Step	Hyp	Ref	Expression
1		reefcl	$$⊢A\in ℝ\to {\mathrm{e}}^A\in ℝ$$
2		efgt0	$$⊢A\in ℝ\to 0<{\mathrm{e}}^A$$
3	1 2	elrpd	$$⊢A\in ℝ\to {\mathrm{e}}^A\in {ℝ}^{+}$$