Metamath Proof Explorer


Theorem nodmord

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 )

Proof

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 )