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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 4378 | . 2 ⊢ (Ord 𝐴 → Tr 𝐴) | |
2 | df-tr 4102 | . 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴) | |
3 | 1, 2 | sylib 122 | 1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ⊆ wss 3129 ∪ cuni 3809 Tr wtr 4101 Ord word 4362 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 |
This theorem depends on definitions: df-bi 117 df-tr 4102 df-iord 4366 |
This theorem is referenced by: ordunisuc2r 4513 limom 4613 |
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