Theorem zre

Description: An integer is a real. (Contributed by NM, 8-Jan-2002)

	Ref	Expression
Assertion	zre	$$⊢N\in \mathbb{Z}\to N\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		elz	$$⊢N\in \mathbb{Z}\leftrightarrow \left(N\in ℝ\wedge \left(N=0\vee N\in \mathbb{N}\vee -N\in \mathbb{N}\right)\right)$$
2	1	simplbi	$$⊢N\in \mathbb{Z}\to N\in ℝ$$