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	$$⊢\phi \to A\in ℝ$$
Assertion	reefcld	$$⊢\phi \to {\mathrm{e}}^A\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		reefcld.1	$$⊢\phi \to A\in ℝ$$
2		reefcl	$$⊢A\in ℝ\to {\mathrm{e}}^A\in ℝ$$
3	1 2	syl	$$⊢\phi \to {\mathrm{e}}^A\in ℝ$$