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