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 0 ⊆ ℕ0*

Proof

Step Hyp Ref Expression
1 ssun1 0 ⊆ ( ℕ0 ∪ { +∞ } )
2 df-xnn0 0* = ( ℕ0 ∪ { +∞ } )
3 1 2 sseqtrri 0 ⊆ ℕ0*