Theorem nn0zd

Description: A nonnegative integer is an integer. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	nn0zd.1	$$⊢\phi \to A\in {\mathbb{N}}_0$$
Assertion	nn0zd	$$⊢\phi \to A\in \mathbb{Z}$$

Proof

Step	Hyp	Ref	Expression
1		nn0zd.1	$$⊢\phi \to A\in {\mathbb{N}}_0$$
2		nn0ssz	$$⊢{\mathbb{N}}_0\subseteq \mathbb{Z}$$
3	2 1	sselid	$$⊢\phi \to A\in \mathbb{Z}$$