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Mirrors > Home > ILE Home > Th. List > pwpwssunieq | Unicode version |
Description: The class of sets whose union is equal to a given class is included in the double power class of that class. (Contributed by BJ, 29-Apr-2021.) |
Ref | Expression |
---|---|
pwpwssunieq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimss 3146 | . . 3 | |
2 | 1 | ss2abi 3164 | . 2 |
3 | pwpwab 3895 | . 2 | |
4 | 2, 3 | sseqtrri 3127 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 cab 2123 wss 3066 cpw 3505 cuni 3731 |
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-v 2683 df-in 3072 df-ss 3079 df-pw 3507 df-uni 3732 |
This theorem is referenced by: toponsspwpwg 12178 dmtopon 12179 |
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