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 ) |
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 ) |