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Metamath Proof Explorer

Theorem nnnn0

Description: A positive integer is a nonnegative integer. (Contributed by NM, 9-May-2004)

Ref Expression
Assertion nnnn0 ( 𝐴 ∈ ℕ → 𝐴 ∈ ℕ0 )

Proof

Step Hyp Ref Expression
1 nnssnn0 ⊢ ℕ ⊆ ℕ0
2 1 sseli ⊢ ( 𝐴 ∈ ℕ → 𝐴 ∈ ℕ0 )