Metamath Proof Explorer


Theorem onuni

Description: The union of an ordinal number is an ordinal number. (Contributed by NM, 29-Sep-2006)

Ref Expression
Assertion onuni ( 𝐴 ∈ On → 𝐴 ∈ On )

Proof

Step Hyp Ref Expression
1 onss ( 𝐴 ∈ On → 𝐴 ⊆ On )
2 ssonuni ( 𝐴 ∈ On → ( 𝐴 ⊆ On → 𝐴 ∈ On ) )
3 1 2 mpd ( 𝐴 ∈ On → 𝐴 ∈ On )