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Mirrors > Home > ILE Home > Th. List > 2pwuninelg | Unicode version |
Description: The power set of 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 Jim Kingdon, 14-Jan-2020.) |
Ref | Expression |
---|---|
2pwuninelg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | en2lp 4407 |
. 2
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2 | pwuni 4056 |
. . . 4
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3 | elpwg 3465 |
. . . 4
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4 | 2, 3 | mpbiri 167 |
. . 3
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5 | ax-ia3 107 |
. . 3
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6 | 4, 5 | syl 14 |
. 2
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7 | 1, 6 | mtoi 631 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-setind 4390 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-v 2643 df-dif 3023 df-un 3025 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-pr 3481 df-uni 3684 |
This theorem is referenced by: mnfnre 7680 |
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