Theorem nn0absid

Description: A nonnegative integer is its own absolute value. (Contributed by AV, 22-Nov-2025)

	Ref	Expression
Assertion	nn0absid	$$⊢N\in {\mathbb{N}}_0\to \left|N\right|=N$$

Proof

Step	Hyp	Ref	Expression
1		nn0re	$$⊢N\in {\mathbb{N}}_0\to N\in ℝ$$
2		nn0ge0	$$⊢N\in {\mathbb{N}}_0\to 0\le N$$
3	1 2	absidd	$$⊢N\in {\mathbb{N}}_0\to \left|N\right|=N$$