Metamath Proof Explorer


Theorem nn0absidi

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

Ref Expression
Hypothesis nn0absidi.i ⊢ 𝑁 ∈ ℕ0
Assertion nn0absidi ( abs ‘ 𝑁 ) = 𝑁

Proof

Step Hyp Ref Expression
1 nn0absidi.i ⊢ 𝑁 ∈ ℕ0
2 nn0absid ⊢ ( 𝑁 ∈ ℕ0 → ( abs ‘ 𝑁 ) = 𝑁 )
3 1 2 ax-mp ⊢ ( abs ‘ 𝑁 ) = 𝑁