Description: An ordinal class includes its union. (Contributed by NM, 13-Sep-2003)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | orduniss | ⊢ ( Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴 ) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | ordtr | ⊢ ( Ord 𝐴 → Tr 𝐴 ) | |
| 2 | df-tr | ⊢ ( Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴 ) | |
| 3 | 1 2 | sylib | ⊢ ( Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴 ) |