Description: The domain of a surreal has the ordinal property. (Contributed by Scott Fenton, 16-Jun-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | nodmord | ⊢ ( 𝐴 ∈ No → Ord dom 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nodmon | ⊢ ( 𝐴 ∈ No → dom 𝐴 ∈ On ) | |
2 | eloni | ⊢ ( dom 𝐴 ∈ On → Ord dom 𝐴 ) | |
3 | 1 2 | syl | ⊢ ( 𝐴 ∈ No → Ord dom 𝐴 ) |