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Mirrors > Home > ILE Home > Th. List > pwuninel2 | Unicode version |
Description: The power set of the union of a set does not belong to the set. This theorem provides a way of constructing a new set that doesn't belong to a given set. (Contributed by Stefan O'Rear, 22-Feb-2015.) |
Ref | Expression |
---|---|
pwuninel2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwnss 4083 | . 2 | |
2 | elssuni 3764 | . 2 | |
3 | 1, 2 | nsyl 617 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wcel 1480 wss 3071 cpw 3510 cuni 3736 |
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-in1 603 ax-in2 604 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 2121 ax-sep 4046 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-nel 2404 df-rab 2425 df-v 2688 df-in 3077 df-ss 3084 df-pw 3512 df-uni 3737 |
This theorem is referenced by: pnfnre 7807 |
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