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Mirrors > Home > ILE Home > Th. List > orduniss | 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 4338 | . 2 ⊢ (Ord 𝐴 → Tr 𝐴) | |
2 | df-tr 4063 | . 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴) | |
3 | 1, 2 | sylib 121 | 1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ⊆ wss 3102 ∪ cuni 3772 Tr wtr 4062 Ord word 4322 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 |
This theorem depends on definitions: df-bi 116 df-tr 4063 df-iord 4326 |
This theorem is referenced by: ordunisuc2r 4472 limom 4572 |
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