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	⊢ e ∈ ℝ

Proof

Step	Hyp	Ref	Expression
1		df-e	⊢ e = ( exp ‘ 1 )
2		1re	⊢ 1 ∈ ℝ
3		reefcl	⊢ ( 1 ∈ ℝ → ( exp ‘ 1 ) ∈ ℝ )
4	2 3	ax-mp	⊢ ( exp ‘ 1 ) ∈ ℝ
5	1 4	eqeltri	⊢ e ∈ ℝ