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Theorem pwidg 4025
Description: Membership of the original in a power set. (Contributed by Stefan O'Rear, 1-Feb-2015.)
Assertion
Ref Expression
pwidg

Proof of Theorem pwidg
StepHypRef Expression
1 ssid 3522 . 2
2 elpwg 4020 . 2
31, 2mpbiri 233 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  e.wcel 1818  C_wss 3475  ~Pcpw 4012
This theorem is referenced by:  pwid  4026  axpweq  4629  knatar  6253  brwdom2  8020  pwwf  8246  rankpwi  8262  canthp1lem2  9052  canthp1  9053  grothpw  9225  mremre  15001  submre  15002  baspartn  19455  fctop  19505  cctop  19507  ppttop  19508  epttop  19510  isopn3  19567  mretopd  19593  tsmsfbas  20626  gsumesum  28067  esumcst  28071  pwsiga  28130  prsiga  28131  sigainb  28136  neibastop1  30177  neibastop2lem  30178  elrfi  30626  dvnprodlem3  31745
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  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-v 3111  df-in 3482  df-ss 3489  df-pw 4014
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