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Metamath Proof Explorer

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	$⊢ e \in ℝ$

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