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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 3857 | 1 ⊢ (𝐴 ∈ On → ∪ {𝑥 ∈ On ∣ 𝑥 ⊆ 𝐴} = 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1363 ∈ wcel 2159 {crab 2471 ⊆ wss 3143 ∪ cuni 3823 Oncon0 4377 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2170 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2175 df-cleq 2181 df-clel 2184 df-nfc 2320 df-ral 2472 df-rab 2476 df-v 2753 df-in 3149 df-ss 3156 df-uni 3824 |
This theorem is referenced by: (None) |
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