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Metamath Proof Explorer

Theorem nn0xnn0

Description: A standard nonnegative integer is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020)

Ref Expression
Assertion nn0xnn0 ( 𝐴 ∈ ℕ0 → 𝐴 ∈ ℕ0* )

Proof

Step Hyp Ref Expression
1 nn0ssxnn0 ⊢ ℕ0 ⊆ ℕ0*
2 1 sseli ⊢ ( 𝐴 ∈ ℕ0 → 𝐴 ∈ ℕ0* )