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Theorem elpwg 3524
 Description: Membership in a power class. Theorem 86 of [Suppes] p. 47. (Contributed by NM, 6-Aug-2000.)
Assertion
Ref Expression
elpwg

Proof of Theorem elpwg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2203 . 2
2 sseq1 3126 . 2
3 vex 2693 . . 3
43elpw 3522 . 2
51, 2, 4vtoclbg 2751 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wcel 1481   wss 3077  cpw 3516 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-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 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-in 3083  df-ss 3090  df-pw 3518 This theorem is referenced by:  elpwi  3525  elpwb  3526  pwidg  3530  prsspwg  3688  elpw2g  4090  snelpwi  4144  prelpwi  4146  pwel  4150  eldifpw  4408  f1opw2  5987  2pwuninelg  6191  tfrlemibfn  6236  tfr1onlembfn  6252  tfrcllembfn  6265  elpmg  6569  fopwdom  6741  fiinopn  12244  ssntr  12364
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