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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcpw | GIF version |
Description: The power class of a bounded class is bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdcpw.1 | ⊢ BOUNDED 𝐴 |
Ref | Expression |
---|---|
bdcpw | ⊢ BOUNDED 𝒫 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcpw.1 | . . . 4 ⊢ BOUNDED 𝐴 | |
2 | 1 | bdss 13062 | . . 3 ⊢ BOUNDED 𝑥 ⊆ 𝐴 |
3 | 2 | bdcab 13047 | . 2 ⊢ BOUNDED {𝑥 ∣ 𝑥 ⊆ 𝐴} |
4 | df-pw 3512 | . 2 ⊢ 𝒫 𝐴 = {𝑥 ∣ 𝑥 ⊆ 𝐴} | |
5 | 3, 4 | bdceqir 13042 | 1 ⊢ BOUNDED 𝒫 𝐴 |
Colors of variables: wff set class |
Syntax hints: {cab 2125 ⊆ wss 3071 𝒫 cpw 3510 BOUNDED wbdc 13038 |
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-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-bd0 13011 ax-bdal 13016 ax-bdsb 13020 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-ral 2421 df-in 3077 df-ss 3084 df-pw 3512 df-bdc 13039 |
This theorem is referenced by: (None) |
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