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Metamath Proof Explorer

Theorem nnnn0i

Description: A positive integer is a nonnegative integer. (Contributed by NM, 20-Jun-2005)

Ref Expression
Hypothesis nnnn0i.1 ⊢ 𝑁 ∈ ℕ
Assertion nnnn0i 𝑁 ∈ ℕ0

Proof

Step Hyp Ref Expression
1 nnnn0i.1 ⊢ 𝑁 ∈ ℕ
2 nnnn0 ⊢ ( 𝑁 ∈ ℕ → 𝑁 ∈ ℕ0 )
3 1 2 ax-mp ⊢ 𝑁 ∈ ℕ0