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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 3782. (Contributed by NM, 17-Nov-2008.) (Proof shortened by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
pwne |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwnss 4132 | . 2 | |
2 | eqimss 3191 | . . 3 | |
3 | 2 | necon3bi 2384 | . 2 |
4 | 1, 3 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wcel 2135 wne 2334 wss 3111 cpw 3553 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-sep 4094 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-nel 2430 df-rab 2451 df-v 2723 df-in 3117 df-ss 3124 df-pw 3555 |
This theorem is referenced by: pnfnemnf 7944 |
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