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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 )