Theorem nnzd

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

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

Proof

Step	Hyp	Ref	Expression
1		nnzd.1	$$⊢\phi \to A\in \mathbb{N}$$
2	1	nnnn0d	$$⊢\phi \to A\in {\mathbb{N}}_0$$
3	2	nn0zd	$$⊢\phi \to A\in \mathbb{Z}$$