Metamath Proof Explorer


Theorem nnsdom

Description: A natural number is strictly dominated by the set of natural numbers. Example 3 of Enderton p. 146. (Contributed by NM, 28-Oct-2003)

Ref Expression
Assertion nnsdom ( 𝐴 ∈ ω → 𝐴 ≺ ω )

Proof

Step Hyp Ref Expression
1 omex ω ∈ V
2 nnsdomg ( ( ω ∈ V ∧ 𝐴 ∈ ω ) → 𝐴 ≺ ω )
3 1 2 mpan ( 𝐴 ∈ ω → 𝐴 ≺ ω )