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 ) |