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Metamath Proof Explorer

Theorem nn0ssxnn0

Description: The standard nonnegative integers are a subset of the extended nonnegative integers. (Contributed by AV, 10-Dec-2020)

Ref Expression
Assertion nn0ssxnn0 ⊢ ℕ 0 ⊆ ℕ 0 *

Proof

Step Hyp Ref Expression
1 ssun1 ⊢ ℕ 0 ⊆ ℕ 0 ∪ +∞
2 df-xnn0 ⊢ ℕ 0 * = ℕ 0 ∪ +∞
3 1 2 sseqtrri ⊢ ℕ 0 ⊆ ℕ 0 *