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Theorem elpw 3728
 Description: Membership in a power class. Theorem 86 of [Suppes] p. 47. (Contributed by NM, 31-Dec-1993.)
Hypothesis
Ref Expression
elpw.1
Assertion
Ref Expression
elpw

Proof of Theorem elpw
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elpw.1 . 2
2 sseq1 3292 . 2
3 df-pw 3724 . 2
41, 2, 3elab2 2988 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wcel 1710  cvv 2859   wss 3257  cpw 3722 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-pw 3724 This theorem is referenced by:  elpwg  3729  prsspw  3878  pwpr  3883  pwtp  3884  pwv  3886  sspwuni  4051  iinpw  4054  iunpwss  4055  snelpwg  4114  snelpwi  4116  unipw  4117  sspwb  4118  pwadjoin  4119  elpw1  4144  dfpw2  4327  eqpw1relk  4479  nnadjoinpw  4521  tfinnnlem1  4533  pw1fnf1o  5855  mapexi  6003  mapval2  6018  mapsspm  6021  mapsspw  6022  enpw1pw  6075  enprmaplem5  6080  enprmaplem6  6081
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