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Theorem snelpwi 4697
 Description: A singleton of a set belongs to the power class of a class containing the set. (Contributed by Alan Sare, 25-Aug-2011.)
Assertion
Ref Expression
snelpwi

Proof of Theorem snelpwi
StepHypRef Expression
1 snssi 4174 . 2
2 snex 4693 . . 3
32elpw 4018 . 2
41, 3sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  e.wcel 1818  C_wss 3475  ~Pcpw 4012  {csn 4029 This theorem is referenced by:  unipw  4702  canth2  7690  unifpw  7843  marypha1lem  7913  infpwfidom  8430  ackbij1lem4  8624  acsfn  15056  sylow2a  16639  dissnref  20029  dissnlocfin  20030  locfindis  20031  txdis  20133  txdis1cn  20136  symgtgp  20600  dispcmp  27862  esumcst  28071  cntnevol  28199  coinflippvt  28423  onsucsuccmpi  29908  lpirlnr  31066  lincvalsng  33017  snlindsntor  33072  unipwrVD  33632  unipwr  33633  pclfinN  35624 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-pw 4014  df-sn 4030  df-pr 4032
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