Metamath Proof Explorer


Theorem piord

Description: A positive integer is ordinal. (Contributed by NM, 29-Jan-1996) (New usage is discouraged.)

Ref Expression
Assertion piord ( 𝐴 ∈ N → Ord 𝐴 )

Proof

Step Hyp Ref Expression
1 pinn ⊢ ( 𝐴 ∈ N → 𝐴 ∈ ω )
2 nnord ⊢ ( 𝐴 ∈ ω → Ord 𝐴 )
3 1 2 syl ⊢ ( 𝐴 ∈ N → Ord 𝐴 )