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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 6205 | . 2 ⊢ (Ord 𝐴 → Tr 𝐴) | |
2 | df-tr 5173 | . 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴) | |
3 | 1, 2 | sylib 220 | 1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊆ wss 3936 ∪ cuni 4838 Tr wtr 5172 Ord word 6190 |
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 209 df-an 399 df-tr 5173 df-ord 6194 |
This theorem is referenced by: orduniorsuc 7545 onfununi 7978 rankuniss 9295 r1limwun 10158 ontgval 33779 |
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