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Mirrors > Home > ILE Home > Th. List > onuniss2 | GIF version |
Description: The union of the ordinal subsets of an ordinal number is that number. (Contributed by Jim Kingdon, 2-Aug-2019.) |
Ref | Expression |
---|---|
onuniss2 | ⊢ (𝐴 ∈ On → ∪ {𝑥 ∈ On ∣ 𝑥 ⊆ 𝐴} = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unimax 3765 | 1 ⊢ (𝐴 ∈ On → ∪ {𝑥 ∈ On ∣ 𝑥 ⊆ 𝐴} = 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1331 ∈ wcel 1480 {crab 2418 ⊆ wss 3066 ∪ cuni 3731 Oncon0 4280 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rab 2423 df-v 2683 df-in 3072 df-ss 3079 df-uni 3732 |
This theorem is referenced by: (None) |
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