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Theorem pwne 4094
 Description: No set equals its power set. The sethood antecedent is necessary; compare pwv 3745. (Contributed by NM, 17-Nov-2008.) (Proof shortened by Mario Carneiro, 23-Dec-2016.)
Assertion
Ref Expression
pwne

Proof of Theorem pwne
StepHypRef Expression
1 pwnss 4093 . 2
2 eqimss 3158 . . 3
32necon3bi 2360 . 2
41, 3syl 14 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wcel 1481   wne 2310   wss 3078  cpw 3517 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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2123  ax-sep 4056 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338  df-nf 1438  df-sb 1738  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-ne 2311  df-nel 2406  df-rab 2427  df-v 2693  df-in 3084  df-ss 3091  df-pw 3519 This theorem is referenced by:  pnfnemnf  7873
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