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	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	reefcld	⊢ ( 𝜑 → ( exp ‘ 𝐴 ) ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		reefcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		reefcl	⊢ ( 𝐴 ∈ ℝ → ( exp ‘ 𝐴 ) ∈ ℝ )
3	1 2	syl	⊢ ( 𝜑 → ( exp ‘ 𝐴 ) ∈ ℝ )