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Mirrors > Home > MPE Home > Th. List > orduniss | Structured version Visualization version GIF version |
Description: An ordinal class includes its union. (Contributed by NM, 13-Sep-2003.) |
Ref | Expression |
---|---|
orduniss | ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordtr 6280 | . 2 ⊢ (Ord 𝐴 → Tr 𝐴) | |
2 | df-tr 5192 | . 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴) | |
3 | 1, 2 | sylib 217 | 1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊆ wss 3887 ∪ cuni 4839 Tr wtr 5191 Ord word 6265 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tr 5192 df-ord 6269 |
This theorem is referenced by: orduniorsuc 7677 onfununi 8172 rankuniss 9624 r1limwun 10492 ontgval 34620 |
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