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Mirrors > Home > ILE Home > Th. List > pwunim | Unicode version |
Description: The power class of the union of two classes equals the union of their power classes, iff one class is a subclass of the other. Part of Exercise 7(b) of [Enderton] p. 28. (Contributed by Jim Kingdon, 30-Sep-2018.) |
Ref | Expression |
---|---|
pwunim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwssunim 4201 | . . 3 | |
2 | pwunss 4200 | . . . 4 | |
3 | 2 | biantru 300 | . . 3 |
4 | 1, 3 | sylib 121 | . 2 |
5 | eqss 3107 | . 2 | |
6 | 4, 5 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 697 wceq 1331 cun 3064 wss 3066 cpw 3505 |
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-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 |
This theorem is referenced by: (None) |
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