Theorem ere

Description: Euler's constant _e = 2.71828... is a real number. (Contributed by NM, 19-Mar-2005) (Revised by Steve Rodriguez, 8-Mar-2006)

	Ref	Expression
Assertion	ere	$$⊢\mathrm{e}\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		df-e	$$⊢\mathrm{e}={\mathrm{e}}^1$$
2		1re	$$⊢1\in ℝ$$
3		reefcl	$$⊢1\in ℝ\to {\mathrm{e}}^1\in ℝ$$
4	2 3	ax-mp	$$⊢{\mathrm{e}}^1\in ℝ$$
5	1 4	eqeltri	$$⊢\mathrm{e}\in ℝ$$