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Mirrors > Home > ILE Home > Th. List > pwne | Unicode version |
Description: No set equals its power set. The sethood antecedent is necessary; compare pwv 3730. (Contributed by NM, 17-Nov-2008.) (Proof shortened by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
pwne |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwnss 4078 | . 2 | |
2 | eqimss 3146 | . . 3 | |
3 | 2 | necon3bi 2356 | . 2 |
4 | 1, 3 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wcel 1480 wne 2306 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-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 2119 ax-sep 4041 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-nel 2402 df-rab 2423 df-v 2683 df-in 3072 df-ss 3079 df-pw 3507 |
This theorem is referenced by: pnfnemnf 7813 |
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