Theorem nnssnn0

Description: Positive naturals are a subset of nonnegative integers. (Contributed by Raph Levien, 10-Dec-2002)

	Ref	Expression
Assertion	nnssnn0	$$⊢\mathbb{N}\subseteq {\mathbb{N}}_0$$

Proof

Step	Hyp	Ref	Expression
1		ssun1	$$⊢\mathbb{N}\subseteq \mathbb{N}\cup \left\{0\right\}$$
2		df-n0	$$⊢{\mathbb{N}}_0=\mathbb{N}\cup \left\{0\right\}$$
3	1 2	sseqtrri	$$⊢\mathbb{N}\subseteq {\mathbb{N}}_0$$